A333012 Integers which can be written in exactly two ways as a sum of two distinct nonzero pentagonal numbers.

211, 215, 381, 447, 602, 663, 766, 807, 853, 874, 1002, 1172, 1197, 1248, 1259, 1372, 1427, 1457, 1571, 1612, 1622, 1639, 1652, 1665, 1752, 1862, 1927, 1996, 2047, 2152, 2245, 2297, 2302, 2332, 2351, 2415, 2472, 2497, 2506, 2523, 2618, 2887, 2912, 2952

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

211 = P(5) + P(11) = P(1) + P(12) = 35 + 176 = 1 + 210, where P(n) is the n-th pentagonal number A000326.

Maple

filter:= proc(n) local X, Y;
    nops(select(proc(s) local x, y; x:= subs(s, X); y:= subs(s, Y);
          x > 0 and y > x and x mod 6 = 5 and y mod 6 = 5 end proc,
[isolve(24*n+2 = X^2 + Y^2)])) = 2
end proc:
select(filter, [$1..3000]); # Robert Israel, Dec 28 2025

Prog

(PARI) is(k) = sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5) == 2; \\ Jinyuan Wang, Mar 06 2020

Crossrefs

Cf. A000326, A333011, A333013, A333014, A333015.

Sequence in context: A031780 A036232 A064826 * A136601 A108406 A051268

Adjacent sequences: A333009 A333010 A333011 * A333013 A333014 A333015

Keyword

nonn

Author

Olivier Gérard, Mar 05 2020

Status

approved