A137318 Concatenation of segments of the digit sequence 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3....

1, 31, 313, 1313, 13131, 313131, 3131313, 13131313, 131313131, 3131313131, 31313131313, 131313131313, 1313131313131, 31313131313131, 313131313131313, 1313131313131313, 13131313131313131, 313131313131313131

Offset: 1

Author

Ctibor O. Zizka, Apr 06 2008

Keywords

• nonn
• base
• easy

Comments

A000042 is 1,11,111,1111,11111,... concatenation of 111111111111111....

A002276 is 2,22,222,2222,22222,... concatenation of 222222222222222....

A133013 is 2,35,71113,... concatenation of 2 3 5 7 11 13 17 19 23 29,...

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000042.

Programs

Mathematica

Module[{nn=20},FromDigits/@TakeList[PadRight[{},(nn(nn+1))/2,{1,3}],Range[ nn]]] (* Harvey P. Dale, Aug 04 2021 *)

Formula

O.g.f.: x*(100x^4 + 200x^3 + 83x^2 + 20x + 1)/((10x-1)(100x^2+1)(x-1)(x^2+1)). - R. J. Mathar, Apr 09 2008

Extensions

More terms from R. J. Mathar, Apr 09 2008