A096057 a(1) = 1, a(n) = least prime divisor of b(n), where b(1) = 1, b(n) = n*b(n-1) + 1 = A002627(n).

1, 3, 2, 41, 2, 1237, 2, 29, 2, 43, 2, 5, 2, 5, 2, 35951249665217, 2, 28001, 2, 1409, 2, 5, 2, 5, 2, 47, 2, 661, 2, 13, 2, 5, 2, 5, 2, 13, 2, 13, 2, 73, 2, 5, 2, 5, 2, 71, 2, 2437159, 2, 31, 2, 5, 2, 5, 2, 13, 2, 3020497643, 2, 23, 2, 5, 2, 5, 2, 5672529813439, 2, 15336863

Offset: 1

Author

Amarnath Murthy, Jun 17 2004

Keywords

• nonn

Examples

			a(4) = 41 because b(3) = 3*b(2)+1 = 3*3+1 = 10 and 4*10+1 = 41, which is prime.
b(n) = 1, 3, 10, 41, ... with least prime divisors a(n) = 1, 3, 2, 41, ....
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..97

Crossrefs

Cf. A096058.

Cf. A020639, A002627, A096058.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,a(n+1)+1}; FactorInteger[#][[1,1]]&/@NestList[nxt,{1,1},40][[All,2]] (* The program generates the first 41 terms of the sequence. *) (* Harvey P. Dale, Jun 21 2022 *)

Formula

a(n) = A020639(A002627(n)).

Extensions

Corrected and extended by Ray G. Opao, Aug 02 2004

Edited by Jonathan Sondow, Jan 09 2005

More terms from Michel Marcus, Mar 28 2020

More terms from Giovanni Resta, Mar 28 2020