A057447 a(n+1) = next prime such that a(n+1)-1 | (a(1)...a(n))^3.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 107, 109, 127, 131, 139, 149, 151, 157, 167, 173, 179, 181, 191, 197, 199, 211, 223, 229, 233, 251, 263, 269, 271, 277, 281, 283, 293, 311, 313, 317, 331, 347, 349, 359

Offset: 1

Author

Robert G. Wilson v, Sep 25 2000

Keywords

• nonn

Comments

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007459, A037896, A057448.

Programs

Mathematica

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 ]