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

Author

Pierre CAMI, Aug 23 2004

Keywords

• nonn
• base

Comments

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

Examples

			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).
		

Crossrefs

Cf. A037916.

Programs

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

Extensions

More terms from Klaus Brockhaus, Apr 25 2005

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