A332989 a(n) is the smallest number writable in n different ways as the sum of two distinct nonzero pentagonal numbers.

6, 211, 2999, 13352, 205427, 250927, 1134927, 2177527, 5002427, 6422352, 17349697, 30135652, 45997927, 55075502, 168570052, 130917177, 101275552, 249483677, 441561407, 433742427, 771789552, 1546505052, 1316582177, 1701923302, 2288827477, 1073520852, 3110207127

Offset

1,1

Comments

I conjecture this sequence is infinite.

Links

Giovanni Resta, Table of n, a(n) for n = 1..40

Example

211 can be written 35 + 176 and 1 + 210;
2999 can be written 852 + 2147, 247 + 2752, 117 + 2882;
13352 = P(52) + P(79) = P(29) + P(90) = P(17) + (93) = P(10) + P(94).

Prog

(PARI) a(n) = for(k=1, oo, if(sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5)==n, return(k))); \\ Jinyuan Wang, Mar 06 2020

Crossrefs

Cf. A000326, A332988.

Cf. A093195 (analog sequence for perfect squares).

Sequence in context: A073100 A093536 A002037 * A370128 A030265 A275567

Adjacent sequences: A332986 A332987 A332988 * A332990 A332991 A332992

Keyword

nonn

Author

Olivier Gérard, Mar 05 2020

Extensions

Name clarified by Jinyuan Wang, Mar 06 2020

Terms a(12) and beyond from Giovanni Resta, Mar 08 2020

Status

approved