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

Author

Olivier Gérard, Mar 05 2020

Keywords

• nonn

Comments

I conjecture this sequence is infinite.

Examples

			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).
		

Links

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

Crossrefs

Cf. A000326, A332988.

Cf. A093195 (analog sequence for perfect squares).

Programs

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

Extensions

Name clarified by Jinyuan Wang, Mar 06 2020

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