A019519 Concatenate odd numbers.
1, 13, 135, 1357, 13579, 1357911, 135791113, 13579111315, 1357911131517, 135791113151719, 13579111315171921, 1357911131517192123, 135791113151719212325, 13579111315171921232527, 1357911131517192123252729, 135791113151719212325272931
Offset: 1
References
- S. Smarandoiu, Convergence of Smarandache continued fractions, Abstract 96T-11-195, Abstracts Amer. Math. Soc., 17 (No. 4, 1996), 680.
Links
- X. Chen and M. Le, The Module Periodicity of Smarandache Concatenated Odd Sequence, Smarandache Notions Journal, Vol. 9, No. 1-2. 1998, 103-104.
- H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.
- F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ... , edited by M. Perez, Xiquan Publishing House 2000.
- F. Smarandache, Collected Papers, Vol. II, Tempus Publ. Hse., Bucharest, Romania, 1996.
- Eric Weisstein's World of Mathematics, Consecutive Number Sequences
- Index entries for sequences related to Most Wanted Primes video
Crossrefs
Programs
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Maple
a:= proc(n) a(n):= `if`(n=1, 1, parse(cat(a(n-1), 2*n-1))) end: seq(a(n), n=1..20); # Alois P. Heinz, Jan 13 2021
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Mathematica
nn=20;With[{odds=Range[1,2nn+1,2]},Table[FromDigits[Flatten[ IntegerDigits/@ Take[odds,n]]],{n,nn}]] (* Harvey P. Dale, Aug 14 2014 *) -
PARI
a(n)=my(s=""); for(k=1, n, s=Str(s, 2*k-1)); eval(s); \\ Michel Marcus, Dec 07 2021
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Python
def a(n): return int("".join(map(str, range(1, 2*n, 2)))) print([a(n) for n in range(1, 18)]) # Michael S. Branicky, Jan 13 2021
Formula
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
Extensions
More terms from Erich Friedman
More terms from Harvey P. Dale, Aug 14 2014