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Concatenate (1,n,n,1).
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%I #21 Jun 25 2018 10:35:57

%S 1001,1111,1221,1331,1441,1551,1661,1771,1881,1991,110101,111111,

%T 112121,113131,114141,115151,116161,117171,118181,119191,120201,

%U 121211,122221,123231,124241,125251,126261,127271,128281,129291,130301,131311,132321

%N Concatenate (1,n,n,1).

%H M. F. Hasler, <a href="/A100846/b100846.txt">Table of n, a(n) for n = 0..10000</a> (Terms a(1..9999) from Robert Israel)

%F 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

%e For n = 0, concatenate(1,n,n,1) is 1001 = a(0).

%e For n = 5, concatenate(1,n,n,1) is 1551 = a(5).

%e For n = 10, concatenate(1,n,n,1) is 110101 = a(10).

%p 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);

%p # _Robert Israel_, Dec 30 2015, edited for n=0 by _M. F. Hasler_, Jun 25 2018

%t 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 *)

%o (PARI) A100846(n)=eval(Str(1,n,n,1)) \\ _M. F. Hasler_, Jun 22 2018

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

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

%K nonn,base

%O 0,1

%A _Parthasarathy Nambi_, Jan 07 2005

%E More terms from _Stefan Steinerberger_, Jan 27 2006

%E Definition reworded and missing 1001 added by _M. F. Hasler_, Jun 22 2018