

A303234


Numbers of the form x*(x+1)/2 + 2^y with x and y nonnegative integers.


30



1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 22, 23, 25, 26, 29, 30, 31, 32, 33, 35, 36, 37, 38, 40, 42, 44, 46, 47, 49, 52, 53, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 70, 71, 74, 77, 79, 80
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OFFSET

1,2


COMMENTS

Conjecture: Any integer n > 1 can be written as the sum of two terms of the current sequence.
This is equivalent to the author's conjecture in A303233.


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 + 2^0.
a(2) = 2 with 2 = 1*（1+1）/2 + 2^0 = 0*(0+1)/2 + 2^1.


MATHEMATICA

SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]];
tab={}; Do[Do[If[SQ[8(n2^k)+1], tab=Append[tab, n]; Goto[aa]], {k, 0, Log[2, n]}]; Label[aa], {n, 1, 80}]; Print[tab]


CROSSREFS

Cf. A000079, A000217, A271518, A281976, A299924, A299537, A299794, A300219, A300362, A300396, A300441, A301376, A301391, A301471, A301472, A302920, A302981, A302982, A302983, A302984, A302985, A303233.
Sequence in context: A109234 A267304 A002855 * A175233 A121229 A286291
Adjacent sequences: A303231 A303232 A303233 * A303235 A303236 A303237


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Apr 20 2018


STATUS

approved



