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 A333013 Integers which can be written in exactly three ways as sum of two distinct nonzero pentagonal numbers. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 6 17:31 EDT 2024. Contains 374981 sequences. (Running on oeis4.)