cp's OEIS Frontend

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

%I A332989 #17 Mar 08 2020 21:43:51
%S A332989 6,211,2999,13352,205427,250927,1134927,2177527,5002427,6422352,
%T A332989 17349697,30135652,45997927,55075502,168570052,130917177,101275552,
%U A332989 249483677,441561407,433742427,771789552,1546505052,1316582177,1701923302,2288827477,1073520852,3110207127
%N A332989 a(n) is the smallest number writable in n different ways as the sum of two distinct nonzero pentagonal numbers.
%C A332989 I conjecture this sequence is infinite.
%H A332989 Giovanni Resta, <a href="/A332989/b332989.txt">Table of n, a(n) for n = 1..40</a>
%e A332989 211 can be written 35 + 176 and 1 + 210;
%e A332989 2999 can be written 852 + 2147, 247 + 2752, 117 + 2882;
%e A332989 13352 = P(52) + P(79) = P(29) + P(90) = P(17) + (93) = P(10) + P(94).
%o A332989 (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
%Y A332989 Cf. A000326, A332988.
%Y A332989 Cf. A093195 (analog sequence for perfect squares).
%K A332989 nonn
%O A332989 1,1
%A A332989 _Olivier Gérard_, Mar 05 2020
%E A332989 Name clarified by _Jinyuan Wang_, Mar 06 2020
%E A332989 Terms a(12) and beyond from _Giovanni Resta_, Mar 08 2020