

A303434


Numbers of the form x*(3*x1)/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
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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

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, On universal sums of polygonal numbers, Sci. China Math. 58(2015), no. 7, 13671396.
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.


EXAMPLE

a(1) = 1 with 1 = 0*(3*01)/2 + 3^0.
a(2) = 2 with 2 = 1*(3*11)/2 + 3^0.
a(5) = 6 with 6 = 2*(3*21)/2 + 3^0.
a(6) = 8 with 8 = 2*(3*21)/2 + 3^1.


MATHEMATICA

PenQ[n_]:=PenQ[n]=IntegerQ[Sqrt[24n+1]]&&(n==0Mod[Sqrt[24n+1]+1, 6]==0);
tab={}; Do[Do[If[PenQ[m3^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: A002183 A060306 A158614 * A080823 A117925 A135571
Adjacent sequences: A303431 A303432 A303433 * A303435 A303436 A303437


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Apr 23 2018


STATUS

approved



