login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A303434 Numbers of the form x*(3*x-1)/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 (list; graph; refs; listen; history; text; internal format)
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

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, On universal sums of polygonal numbers, Sci. China Math. 58(2015), no. 7, 1367-1396.

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.

EXAMPLE

a(1) = 1 with 1 = 0*(3*0-1)/2 + 3^0.

a(2) = 2 with 2 = 1*(3*1-1)/2 + 3^0.

a(5) = 6 with 6 = 2*(3*2-1)/2 + 3^0.

a(6) = 8 with 8 = 2*(3*2-1)/2 + 3^1.

MATHEMATICA

PenQ[n_]:=PenQ[n]=IntegerQ[Sqrt[24n+1]]&&(n==0||Mod[Sqrt[24n+1]+1, 6]==0);

tab={}; Do[Do[If[PenQ[m-3^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

Zhi-Wei Sun, Apr 23 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 19 08:49 EDT 2019. Contains 325155 sequences. (Running on oeis4.)