A333013 Integers which can be written in exactly three ways as sum of two distinct nonzero pentagonal numbers.

2999, 6450, 6552, 7177, 8422, 9204, 9652, 10037, 10622, 11380, 11467, 16577, 17652, 17772, 17789, 17818, 19132, 19761, 20177, 21327, 21477, 22277, 22702, 22855, 23008, 23212, 23387, 23427, 23444, 24402, 24662, 25677, 25847, 26286, 26902, 27649, 27802, 27847, 28567, 29927

Offset

1,1

Links

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

Example

2999 = P(24) + P(38) = P(13) + P(43) = P(9) + P(44), where P(n) is the n-th pentagonal number A000326.

Mathematica

dnpQ[n_]:=Count[IntegerPartitions[n, {2}], _?(AllTrue[(1+Sqrt[1+24#])/6, IntegerQ]&)]==3; Parallelize[Select[Range[30000], dnpQ]] (* or *) Select[Tally[Total/@Subsets[ PolygonalNumber[ 5, Range[200]], {2}]], #[[2]]==3&][[;; , 1]]//Union (* Harvey P. Dale, Jul 20 2023 *)

Prog

(PARI) is(k) = sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5) == 3; \\ Jinyuan Wang, Mar 06 2020

Crossrefs

Cf. A000326, A333011, A333012, A333014, A333015.

Sequence in context: A235529 A106766 A119892 * A158861 A329169 A236982

Adjacent sequences: A333010 A333011 A333012 * A333014 A333015 A333016

Keyword

nonn

Author

Olivier Gérard, Mar 05 2020

Status

approved