A364692 -id:A364692 - cp's OEIS frontend

A344989 Smallest number whose number of partitions into n distinct primes is n, or zero if there are no such partitions.

2, 16, 26, 33, 55, 59, 0, 0, 124, 159, 233, 227, 276, 0, 372, 480, 0, 0, 0, 752, 0, 920, 0, 1011, 0, 1211, 1425, 0, 0, 0, 0, 0, 2050, 2336, 2495, 0, 0, 0, 0, 3340, 0, 3712, 0, 0, 4303, 0, 0, 0, 0, 5195, 0, 5669, 0, 6163, 6673, 0, 0, 0, 7504, 0, 0, 8670, 0, 9304, 9623, 0, 0, 0, 10638, 10981, 0, 12062, 0

Offset: 1

Metin Sariyar, Jun 04 2021

From David A. Corneth, Aug 21 2025: (Start)
How to prove a 0? I used the heuristic:
a(n) = 0 if 2*n consecutive integers can be written in strictly more than n ways as a sum of n distinct primes and up to that point no positive integer has exactly n such ways.
What other rules where used? (End)

			a(2) = 16 because 16 is the smallest number whose number of partitions into 2 distinct primes is 2; 16 = 3+13 = 5+11.

Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 233

Cf. A364692 asks for the largest number with the same properties.

Cf. A000586, A077914, A117929, A125688, A219180, A219198, A219199, A219200, A219201, A219202, A219203, A219204.

a(12)-a(20) from Alois P. Heinz, Jun 04 2021

More terms from David A. Corneth, Aug 21 2025

cp's OEIS Frontend

A344989 Smallest number whose number of partitions into n distinct primes is n, or zero if there are no such partitions.

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