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

1,1

Comments

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)

Links

Table of n, a(n) for n=1..73.

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

Example

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

Crossrefs

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

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

Sequence in context: A019317 A355714 A394360 * A276069 A190046 A067566

Adjacent sequences: A344986 A344987 A344988 * A344990 A344991 A344992

Keyword

nonn

Author

Metin Sariyar, Jun 04 2021

Extensions

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

More terms from David A. Corneth, Aug 21 2025

Status

approved