A097463 Let P(i) = i-th prime. To get a(n), factor P(n)-1 as a product of primes, then concatenate the exponents.

0, 1, 2, 11, 101, 21, 4, 12, 10001, 2001, 111, 22, 301, 1101, 100000001, 200001, 1000000001, 211, 11001, 1011, 32, 110001, 1000000000001, 30001, 51, 202, 1100001, 1000000000000001, 23, 4001, 1201, 101001, 3000001, 110000001, 200000000001

Offset

1,3

Comments

If P(n)-1 = P(1)^a * P(2)^b *....* P(j)^k then a(n) = ab...k.

Links

Table of n, a(n) for n=1..35.

Example

3-1=2^1, so a(2)=1.
5-1=2^2, so a(3)=2.
7-1=2^1*3^1, so a(4)=11.
23=(2^1)*(11^1)+1. So a(9) = 10001.
37 = 36 + 1 = 2^2*3^2 + 1, so 37 becomes 22 (a=2,b=2).

Prog

(PARI) {forprime(p=2, 150, f=factor(p-1); j=1; q=2; s="0"; while(j<=matsize(f)[1], if(q==f[j, 1], s=concat(s, f[j, 2]); j++, s=concat(s, 0)); q=nextprime(q+1)); print1(eval(s), ", "))} \\ Klaus Brockhaus, Apr 25 2005

Crossrefs

Cf. A037916.

Sequence in context: A038371 A236174 A003021 * A263607 A083394 A263611

Adjacent sequences: A097460 A097461 A097462 * A097464 A097465 A097466

Keyword

nonn,base

Author

Pierre CAMI, Aug 23 2004

Extensions

More terms from Klaus Brockhaus, Apr 25 2005

a(9) corrected by Dennis (tuesdayist(AT)juno.com), Mar 30 2006

Status

approved