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 A303393 Numbers of the form x*(x+1)/2 + 5^y with x and y nonnegative integers. 29
 1, 2, 4, 5, 6, 7, 8, 11, 15, 16, 20, 22, 25, 26, 28, 29, 31, 33, 35, 37, 40, 41, 46, 50, 53, 56, 60, 61, 67, 70, 71, 79, 80, 83, 91, 92, 96, 103, 106, 110, 116, 121, 125, 126, 128, 130, 131, 135, 137, 140, 141, 145, 146, 153, 154, 158, 161, 170, 172, 176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The author's conjecture in A303389 has the following equivalent version: Each integer n > 1 can be expressed as the sum of two terms of the current sequence. This has been verified for all n = 2..2*10^8. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 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. Zhi-Wei Sun, Restricted sums of four squares, arXiv:1701.05868 [math.NT], 2017-2018. EXAMPLE a(1) = 1 with 1 = 0*(0+1)/2 + 5^0. a(2) = 2 with 2 = 1*(1+1)/2 + 5^0. a(3) = 4 with 4 = 2*(2+1)/2 + 5^0. MATHEMATICA TQ[n_]:=TQ[n]=IntegerQ[Sqrt[8n+1]]; tab={}; Do[Do[If[TQ[m-5^k], tab=Append[tab, m]; Goto[aa]], {k, 0, Log[5, m]}]; Label[aa], {m, 1, 176}]; Print[tab] CROSSREFS Cf. A000217, A000351, A271518, A273812, A281976, A299924, A299537, A299794, A300219, A300362, A300396, A300441, A301376, A301391, A301471, A301472, A302920, A302981, A302982, A302983, A302984, A302985, A303233, A303234, A303235, A303338, A303363, A303389. Sequence in context: A111688 A058049 A091871 * A039085 A302433 A026486 Adjacent sequences:  A303390 A303391 A303392 * A303394 A303395 A303396 KEYWORD nonn AUTHOR Zhi-Wei Sun, Apr 23 2018 STATUS approved

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)