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Problems & Puzzles:
Puzzles
Puzzle 1252 A301339
On March 27, 2018, G. L. Honaker, Jr., created OEIS
sequence
A301339,
that initially included thirteen terms containing
eight combinations of possible
ending-digit concatenations that represent a tie
among the primes counted, i.e., {2, 23, 235, 2357,
12357, 3, 37 & 137}.
a(13) = 137 because primes that end with
digits 1, 3, and 7 occur most frequently (exactly
three times each) up to the 13th prime
From that time, until
November 11, 2025, another eight
concatenations have been solved: {7, 79, 9, 17, 13,
379, 39 & 1} for a total of sixteen
solutions.
Current status of
the A301339:
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1 |
occurs first at |
a(2766290) |
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2 |
occurs first at |
a(1), |
by G. L. H. |
|
3 |
occurs first at |
a(6), |
by G. L. H. |
|
7 |
occurs first at |
a(37) |
|
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9 |
occurs first at |
a(7153) |
|
|
13 |
occurs first at |
a(45532) |
|
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17 |
occurs first at |
a(12655) |
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23 |
occurs first at |
a(2, |
by G. L. H. |
|
37 |
occurs first at |
a(7), |
by G. L. H. |
|
39 |
occurs first at |
a(429687) |
|
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79 |
occurs first at |
a(7042) |
|
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137 |
occurs first at |
a(13), |
by G. L. H. |
|
235 |
occurs first at |
a(3), |
by G. L. H. |
|
379 |
occurs first at |
a(93562) |
|
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2357 |
occurs first at |
a(4), |
by G. L. H. |
|
12357 |
occurs first at |
a(5) |
by G. L. H. |
The other eight terms were
computed, apparently, by Chuck Gaydos.
Later, Michael S. Branicky added the following
comment: "The other possible new terms
are 19, 139, 179 and 1379.". This
comment remarks exactly what are the only
combinations pending to be found.
In short,
from the 20 possible combinations, 16 have been
solved (2, 23, 235, 2357, 12357, 3, 37 & 137 and 7,
79, 9, 17, 13, 379, 39 & 1). Only 4 combinations are
still unsolved (19, 139, 178 & 1379).
Q: Find a first occurrence for each of the four
pending combinations: 19, 139, 179 & 1379
* BTW, according to the following
curio,
G. L. Honaker, Jr. offers $19 USD "to
anyone who finds the first occurrence"
of the combination 19.
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