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A135506 a(n) = x(n+1)/x(n) - 1 where x(1)=1 and x(k) = x(k-1) + lcm(x(k-1),k). 17
2, 1, 2, 5, 1, 7, 1, 1, 5, 11, 1, 13, 1, 5, 1, 17, 1, 19, 1, 1, 11, 23, 1, 5, 13, 1, 1, 29, 1, 31, 1, 11, 17, 1, 1, 37, 1, 13, 1, 41, 1, 43, 1, 1, 23, 47, 1, 1, 1, 17, 13, 53, 1, 1, 1, 1, 29, 59, 1, 61, 1, 1, 1, 13, 1, 67, 1, 23, 1, 71, 1, 73, 1, 1, 1, 1, 13, 79, 1, 1, 41, 83, 1, 1, 43, 29, 1, 89 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence has properties related to primes. For instance: terms consist of 1's or primes only; if 3 never occurs, any prime p occurs finitely many times.

All prime numbers 'p' from the sequence A014963(n), which equals A003418(n+1)/A003418(n), are in a(n-1) = p. - Eric Desbiaux, Jan 11 2015

For any prime p > 3, a(p-1) = p. Also a(n) is not 3 for any n. All terms but a(1) and a(3) are odd, and probably all of them are not composite numbers; this is strongly related to a strong version of Linnik's Theorem (see Ruiz-Cabello link). - Serafín Ruiz-Cabello, Sep 30 2015

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Serafín Ruiz-Cabello, On the use of the lowest common multiple to build a prime-generating recurrence, arXiv:1504.05041 [math.CO], 2015.

MAPLE

x[1]:= 1;

for n from 2 to 101 do

  x[n]:= x[n-1] + ilcm(x[n-1], n);

  a[n-1]:= x[n]/x[n-1]-1;

od:

seq(a[n], n=1..100); # Robert Israel, Jan 11 2015

MATHEMATICA

a[n_] := x[n+1]/x[n] - 1; x[1] = 1; x[k_] := x[k] = x[k-1] + LCM[x[k-1], k]; Table[a[n], {n, 1, 88}] (* Jean-François Alcover, Jan 08 2013 *)

PROG

(PARI) x1=1; for(n=2, 40, x2=x1+lcm(x1, n); t=x1; x1=x2; print1(x2/t-1, ", "))

CROSSREFS

Cf. A106108.

Sequence in context: A210223 A242598 A225568 * A068822 A090079 A165195

Adjacent sequences:  A135503 A135504 A135505 * A135507 A135508 A135509

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Feb 09 2008

STATUS

approved

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Last modified June 28 04:43 EDT 2017. Contains 288813 sequences.