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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).

%I A096057 #24 Oct 29 2024 03:40:22
%S A096057 1,3,2,41,2,1237,2,29,2,43,2,5,2,5,2,35951249665217,2,28001,2,1409,2,
%T A096057 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,
%U A096057 2,31,2,5,2,5,2,13,2,3020497643,2,23,2,5,2,5,2,5672529813439,2,15336863
%N 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).
%H A096057 Amiram Eldar, <a href="/A096057/b096057.txt">Table of n, a(n) for n = 1..97</a>
%F A096057 a(n) = A020639(A002627(n)).
%e A096057 a(4) = 41 because b(3) = 3*b(2)+1 = 3*3+1 = 10 and 4*10+1 = 41, which is prime.
%e A096057 b(n) = 1, 3, 10, 41, ... with least prime divisors a(n) = 1, 3, 2, 41, ....
%t A096057 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 *)
%Y A096057 Cf. A096058.
%Y A096057 Cf. A020639, A002627, A096058.
%K A096057 nonn
%O A096057 1,2
%A A096057 _Amarnath Murthy_, Jun 17 2004
%E A096057 Corrected and extended by _Ray G. Opao_, Aug 02 2004
%E A096057 Edited by _Jonathan Sondow_, Jan 09 2005
%E A096057 More terms from _Michel Marcus_, Mar 28 2020
%E A096057 More terms from _Giovanni Resta_, Mar 28 2020