

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
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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

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, Refining Lagrange's foursquare theorem, J. Number Theory 175(2017), 167190.
ZhiWei Sun, New conjectures on representations of integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), no. 2, 97120.
ZhiWei Sun, Restricted sums of four squares, arXiv:1701.05868 [math.NT], 20172018.


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[m5^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

ZhiWei Sun, Apr 23 2018


STATUS

approved



