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A000422 Concatenation of numbers from n down to 1. 45
1, 21, 321, 4321, 54321, 654321, 7654321, 87654321, 987654321, 10987654321, 1110987654321, 121110987654321, 13121110987654321, 1413121110987654321, 151413121110987654321, 16151413121110987654321, 1716151413121110987654321, 181716151413121110987654321 (list; graph; refs; listen; history; text; internal format)
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

There are no further prime terms up to n=4000. - Daniel Arribas, Jun 04 2016

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[n-1])) + a[n-1]

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=n-1, 1, -1, t=t*10^#Str(k)+k); t \\ Charles R Greathouse IV, Jul 15 2011

(PARI) A000422(n, p=1, L=1)=sum(k=1, n, k*p*=L+(k==L&&!L*=10)) \\ M. F. Hasler, Nov 02 2016

CROSSREFS

Cf. A007908, A058183, A104759, A116504, A116505, 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

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Last modified December 8 01:14 EST 2016. Contains 278902 sequences.