The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 + 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(n-2^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 Zhi-Wei Sun, Apr 20 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 7 13:36 EDT 2020. Contains 333305 sequences. (Running on oeis4.)