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%I #47 Dec 30 2023 23:42:58
%S 1,13,135,1357,13579,1357911,135791113,13579111315,1357911131517,
%T 135791113151719,13579111315171921,1357911131517192123,
%U 135791113151719212325,13579111315171921232527,1357911131517192123252729,135791113151719212325272931
%N Concatenate odd numbers.
%D S. Smarandoiu, Convergence of Smarandache continued fractions, Abstract 96T-11-195, Abstracts Amer. Math. Soc., 17 (No. 4, 1996), 680.
%H X. Chen and M. Le, <a href="https://vixra.org/abs/1403.0868">The Module Periodicity of Smarandache Concatenated Odd Sequence</a>, Smarandache Notions Journal, Vol. 9, No. 1-2. 1998, 103-104.
%H H. Ibstedt, <a href="http://vixra.org/abs/1403.0853">A Few Smarandache Sequences</a>, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Definitions-book.pdf">Definitions, Solved and Unsolved Problems, Conjectures, ... </a>, edited by M. Perez, Xiquan Publishing House 2000.
%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/CP2.pdf">Collected Papers, Vol. II</a>, Tempus Publ. Hse., Bucharest, Romania, 1996.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConsecutiveNumberSequences.html">Consecutive Number Sequences</a>
%H <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>
%F Sequence grows like 10^K, where K = 2 + floor(log_10(n)) + floor(log_10(a(n-1))). More generally we may consider a(n)= F(a(n-1),n)*B^K + G(a(n-1),n); K = floor(log_B H(a(n-1),n)); F(a(n-1),n); G(a(n-1),n); H(a(n-1),n) integer polynomials; B integer. - _Ctibor O. Zizka_, Mar 08 2008
%F Lim_{n->oo} a(n)/A019520(n) = 0 (see A067095). - _Bernard Schott_, Dec 07 2021
%p a:= proc(n) a(n):= `if`(n=1, 1, parse(cat(a(n-1), 2*n-1))) end:
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Jan 13 2021
%t nn=20;With[{odds=Range[1,2nn+1,2]},Table[FromDigits[Flatten[ IntegerDigits/@ Take[odds,n]]],{n,nn}]] (* _Harvey P. Dale_, Aug 14 2014 *)
%o (Python)
%o def a(n): return int("".join(map(str, range(1, 2*n, 2))))
%o print([a(n) for n in range(1, 18)]) # _Michael S. Branicky_, Jan 13 2021
%o (PARI) a(n)=my(s=""); for(k=1, n, s=Str(s, 2*k-1)); eval(s); \\ _Michel Marcus_, Dec 07 2021
%Y Primes are in A048847, while their indices are in A046036.
%Y Cf. A019520 (similar, with even numbers), A067095.
%K base,nonn,easy
%O 1,2
%A R. Muller
%E More terms from _Erich Friedman_
%E More terms from _Harvey P. Dale_, Aug 14 2014
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