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

1,2

Links

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

Formula

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

Example

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, ....

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 *)

Crossrefs

Cf. A096058.

Cf. A020639, A002627, A096058.

Sequence in context: A062743 A370825 A009084 * A179984 A260888 A065085

Adjacent sequences: A096054 A096055 A096056 * A096058 A096059 A096060

Keyword

nonn

Author

Amarnath Murthy, Jun 17 2004

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

Status

approved