%I #16 Sep 09 2023 11:35:08
%S 2,3,5,7,11,13,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,101,
%T 107,109,127,131,139,149,151,157,167,173,179,181,191,197,199,211,223,
%U 229,233,251,263,269,271,277,281,283,293,311,313,317,331,347,349,359
%N a(n+1) = next prime such that a(n+1)-1 | (a(1)...a(n))^3.
%C No prime of the form a*b^k + 1, with a > 0, b > 1 and k > 3 (including those in A037896) belongs to the sequence. - _Mauro Fiorentini_, Aug 09 2023
%H T. D. Noe, <a href="/A057447/b057447.txt">Table of n, a(n) for n = 1..1000</a>
%t NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; f[ n_List ] := (a = n; b = Apply[ Times, a^3 ]; d = NextPrime[ a[[ -1 ]] ]; While[ ! IntegerQ[ b/(d - 1) ] && d < b+2, d = NextPrime[ d ] ]; AppendTo[ a, d ]; Return[ a ]); Nest[ f, {2}, 75 ]
%Y Cf. A007459, A037896, A057448.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 25 2000