A019519 Concatenate odd numbers.

1, 13, 135, 1357, 13579, 1357911, 135791113, 13579111315, 1357911131517, 135791113151719, 13579111315171921, 1357911131517192123, 135791113151719212325, 13579111315171921232527, 1357911131517192123252729, 135791113151719212325272931

Offset

1,2

References

S. Smarandoiu, Convergence of Smarandache continued fractions, Abstract 96T-11-195, Abstracts Amer. Math. Soc., 17 (No. 4, 1996), 680.

Links

Table of n, a(n) for n=1..16.

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

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

Lim_{n->oo} a(n)/A019520(n) = 0 (see A067095). - Bernard Schott, Dec 07 2021

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

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 *)

Prog

(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
(PARI) a(n)=my(s=""); for(k=1, n, s=Str(s, 2*k-1)); eval(s); \\ Michel Marcus, Dec 07 2021

Crossrefs

Primes are in A048847, while their indices are in A046036.

Cf. A019520 (similar, with even numbers), A067095.

Sequence in context: A132930 A130774 A179619 * A243216 A112225 A069511

Adjacent sequences: A019516 A019517 A019518 * A019520 A019521 A019522

Keyword

base,nonn,easy

Author

R. Muller

Extensions

More terms from Erich Friedman

More terms from Harvey P. Dale, Aug 14 2014

Status

approved