A100846 Concatenate (1,n,n,1).

1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 110101, 111111, 112121, 113131, 114141, 115151, 116161, 117171, 118181, 119191, 120201, 121211, 122221, 123231, 124241, 125251, 126261, 127271, 128281, 129291, 130301, 131311, 132321

Offset

0,1

Links

M. F. Hasler, Table of n, a(n) for n = 0..10000 (Terms a(1..9999) from Robert Israel)

Formula

G.f.: 1001 + x*(31-11*x)/(1-x)^2 + Sum_{k>=0} 90*(12*10^(2*k)*(1-x)+10^k*x)*x^(10^k)/(1-x)^2. - Robert Israel, Dec 30 2015

Example

For n = 0, concatenate(1,n,n,1) is 1001 = a(0).
For n = 5, concatenate(1,n,n,1) is 1551 = a(5).
For n = 10, concatenate(1,n,n,1) is 110101 = a(10).

Maple

seq(seq((10^(2*d+1)+1+(10^(d+1)+10)*n), n=`if`(d>1, 10^(d-1), 0) .. 10^d-1), d=1..3);
# Robert Israel, Dec 30 2015, edited for n=0 by M. F. Hasler, Jun 25 2018

Mathematica

For[n = 0, n < 30, n++, l := Floor[Log[10, Min[n, 1]] + 1]; gvout := (n*10^l + n)*10 + 1; m := Floor[Log[10, gvout]]; giveout := 10^(m + 1) + out; Print[giveout]] (* Stefan Steinerberger, Jan 27 2006, edited for n=0 by M. F. Hasler, Jun 25 2018 *)

Prog

(PARI) A100846(n)=eval(Str(1, n, n, 1)) \\ M. F. Hasler, Jun 22 2018

Crossrefs

Cf. A100896 (3nn3), 7nn7 (A100897), 9nn9 (A102484).

For primes in these sequences: A102496, A102497 (1nn1); A102498, A102499 (3nn3); A102500, A102501 (7nn7); A102502, A102503 (9nn9); A102504 (intersection).

Sequence in context: A317291 A362921 A241946 * A153814 A259080 A100709

Adjacent sequences: A100843 A100844 A100845 * A100847 A100848 A100849

Keyword

nonn,base

Author

Parthasarathy Nambi, Jan 07 2005

Extensions

More terms from Stefan Steinerberger, Jan 27 2006

Definition reworded and missing 1001 added by M. F. Hasler, Jun 22 2018

Status

approved