# Fun With Numbers: Consecutive Number And Consecutive Digit Dates

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December 13, 2014 was a perfect example of a consecutive number date. Copyright image by Decoded Science, all rights reserved.

The recent date of 12/13/14 caused quite a stir, especially at hospitals when a baby was born at 10:11. Let’s explore some of the dates that involve consecutive numbers in one form or another.

## First, Some Ground Rules

• We will consider years from one to 9999.
• We will separate dates into two general categories — consecutive number dates (CND) and Consecutive Digit Dates (CDD).
• We will disregard the slashes that separate month/day/year.
• We will break the number of digits down into separate categories.
• We will consider ascending, descending, and cyclic sequences.

Never mind trying to figure out what that means. It will be apparent as we proceed.

## Six-Digit CNDs Of The Form MM/DD/YY or DD/MM/YY

Interest in the recent CND of 12/13/14 was fueled by the fact that there won’t be another like it for over 88 years (01/02/03). There is one date of this type each year from the third through the 14th year of each century, a total of twelve per hundred years.

It is interesting to ask how many of the December 13ths are Fridays. Because the answer is surprising — NONE. It is a strange quirk of the modern calendar that on the same date every hundred years the day of the week is constrained to four. In the case of December 13 of the 14th year of each century, it can only occur on a Tuesday, Thursday, Saturday, or Sunday. There will be no black cats for those born on December thirteenth of the fourteenth year of any century.

In continental representation, there are only 11 CNDs per century, because 12/13/14 is disqualified. In Europe, the date that caused the recent hubbub in America, written there as the innocuous 13/12/14, was virtually ignored.

## CND Birthdays

A person born on the date of 12/13/14 in the 21st century will have his hundredth birthday on 12/13/14 in the 22nd century. And a person born on 01/02/03 could live to see 24 CNDs (12 in each century) if he could make it to 111 years, 11 months and 11 days.

According to several sources, Kane Tanaka of Fukuoka, Japan was born on Jan. 2, 1903, and recently observed the 24th CND during his lifetime. He will be 112 on January 3, 2015. Happy birthday, Kane.

## Eight-Digit CNDs Of The Form MM/DD/YYYY or DD/MM/YYYY

If we represent the year by four digits, which is ever-so-much more precise, the number of CNDs diminishes to a very few. By analogy to the six-digit CNDs, there are twelve in our allowable 9999 year time frame, one each century from 01/02/0304 t0 12/13/1415, and sad to say, we’ve seen the last of them. Here again, the Continentals come up one short.

## Descending CNDs

For CNDs in which the numbers descend rather than ascend, the number of dates narrows slightly: There are only ten six-digit descending CNDs per century, from 12/11/10 to 03/02/01. Here’s where the Europeans get their date back, because they can add 13/12/11 to their list.

Descending eight-digit CNDs are analogous to ascending ones: 12/11/1009 to 03/02/0100, with Europe adding 13/12/1110. In the US, there hasn’t been one of those for over a thousand years — and there’ll never be another.

## Consecutive Digit Dates

If we only consider dates in which the digits are consecutive, interesting things happen. Some CDDs are in the relatively near future.

Six-Digit Ascending CDDs of the form MM/DD/YY or DD/MM/YY:

There is only one date of this form in each century, 01/23/45. Of the dates we’ve looked at, the one of this form in the 21st century is the nearest to the present (considering future dates only). January 21 turns out to be a unique date in the American notation. In the European notation, there are no dates at all of this form.

Six-Digit Descending CDDs of the form MM/DD/YY or DD/MM/YY:

If we think of the number line as being continuous, there are no descending CDDs. However, if we consider the ten digits (including zero) as being cyclic, there is one date each century that becomes a descending CDD, but it is in the European system: 21/09/87. King George’s subjects can celebrate September 9, 2087 without any interference from the wayward colonies.

## Eight-Digit CDDs

If we write the date in the more demanding form MM/DD/YYYY or DD/MM/YYYY, there is only one CDD that qualifies: 01/23/4567. The Europeans are shut out. There are no descending dates in the American notation, but there is a descending cyclic date in the European system: 21/09/8765.

Each of the numbers that comprise this set of unique dates, one in the American and one in the European system, has an interesting property:

• 1234567 has a square root that, to the nearest ten-thousandth, is 1111.111
• 21098765 is a near-prime. It has only two factors, five and 4219753

## Loosening The Rules

Until now, we have insisted on writing each day or month in two-digit form. For example, the number one has been written 01. If we allow a more liberal (and practical) rendering of the single digits without the leading zero, date possibilities open up, so that we may celebrate more fully in the near term.

## Six-Digit CNDs Of The Form M/D/YYYY Or D/M/YYYY In The Near Future

• The ascending CND 1/9/2021 is only a little more than six years in the future. It beats out the European interpretation of the date by several months.
• The descending CND 2/1/2019 is just over four years hence, but the Europeans get to celebrate thirty days earlier.

We have plenty of time to plan the party.

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