

A000422


Concatenation of numbers from n down to 1.


41



1, 21, 321, 4321, 54321, 654321, 7654321, 87654321, 987654321, 10987654321, 1110987654321, 121110987654321, 13121110987654321, 1413121110987654321, 151413121110987654321, 16151413121110987654321, 1716151413121110987654321, 181716151413121110987654321
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OFFSET

1,2


COMMENTS

The first prime term in this sequence is a(82).  Artur Jasinski, Mar 30 2008
For n < 10^4, a(n)/A000217(n) is an integer for n = 1, 2, and 18. The integers are 1, 7 (prime), and 1062667552123515268933651, respectively.  Derek Orr, Sep 04 2014


REFERENCES

F. Smarandache, "Properties of the Numbers", University of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ


LINKS

T. D. Noe, Table of n, a(n) for n = 1..150
R. W. Stephan, Factors and primes in two Smarandache sequences
Eric Weisstein's World of Mathematics, Consecutive Number Sequences


FORMULA

a(n+1) = (n+1)*10^len(a(n)) + a(n), where len(k) = number of digits in k.


MAPLE

a[1]:= 1:
for n from 2 to 100 do
a[n]:= n*10^(1+ilog10(a[n1])) + a[n1]
od:
seq(a[n], n=1..100); # Robert Israel, Sep 05 2014


MATHEMATICA

b = {}; a = {}; Do[w = RealDigits[n]; w = First[w]; Do[PrependTo[a, w[[Length[w]  k + 1]]], {k, 1, Length[w]}]; p = FromDigits[a]; AppendTo[b, p], {n, 1, 30}]; b (* Artur Jasinski, Mar 30 2008 *)


PROG

(PARI) a(n)=my(t=n); forstep(k=n1, 1, 1, t=t*10^#Str(k)+k); t \\ Charles R Greathouse IV, Jul 15 2011


CROSSREFS

Cf. A000422, A116504, A007908, A116505, A104759, A138789, A138790, A138793.
Sequence in context: A104759 A138793 A014925 * A060554 A057610 A036737
Adjacent sequences: A000419 A000420 A000421 * A000423 A000424 A000425


KEYWORD

nonn,base


AUTHOR

R. Muller


STATUS

approved



