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 A303434 Numbers of the form x*(3*x-1)/2 + 3^y with x and y nonnegative integers. 24
 1, 2, 3, 4, 6, 8, 9, 10, 13, 14, 15, 21, 23, 25, 27, 28, 31, 32, 36, 38, 39, 44, 49, 52, 54, 60, 62, 71, 73, 78, 79, 81, 82, 86, 93, 95, 97, 101, 103, 116, 118, 119, 120, 126, 132, 144, 146, 148, 151, 154, 172, 173, 177, 179, 185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The author's conjecture in A303401 has the following equivalent version: Each integer n > 1 can be written as the sum of two terms of the current sequence. This has been verified for all n = 2..7*10^6. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, On universal sums of polygonal numbers, Sci. China Math. 58(2015), no. 7, 1367-1396. Zhi-Wei Sun, Refining Lagrange's four-square theorem, J. Number Theory 175(2017), 167-190. Zhi-Wei Sun, New conjectures on representations of integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), no. 2, 97-120. EXAMPLE a(1) = 1 with 1 = 0*(3*0-1)/2 + 3^0. a(2) = 2 with 2 = 1*(3*1-1)/2 + 3^0. a(5) = 6 with 6 = 2*(3*2-1)/2 + 3^0. a(6) = 8 with 8 = 2*(3*2-1)/2 + 3^1. MATHEMATICA PenQ[n_]:=PenQ[n]=IntegerQ[Sqrt[24n+1]]&&(n==0||Mod[Sqrt[24n+1]+1, 6]==0); tab={}; Do[Do[If[PenQ[m-3^k], n=n+1; tab=Append[tab, m]; Goto[aa]], {k, 0, Log[3, m]}]; Label[aa], {m, 1, 185}]; Print[tab] CROSSREFS Cf. A000244, A000326, A303233, A303234, A303338, A303363, A303389, A303393, A303399, A303428, A303401, A303432. Sequence in context: A349607 A060306 A158614 * A080823 A117925 A135571 Adjacent sequences: A303431 A303432 A303433 * A303435 A303436 A303437 KEYWORD nonn AUTHOR Zhi-Wei Sun, Apr 23 2018 STATUS approved

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Last modified February 3 02:45 EST 2023. Contains 360024 sequences. (Running on oeis4.)