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