A290427 Rearrangement of primes such that every partial product minus 1 is a prime.

3, 2, 5, 13, 7, 11, 19, 43, 79, 31, 17, 71, 89, 23, 41, 67, 29, 73, 83, 107, 59, 53, 239, 101, 109, 233, 61, 197, 97, 103, 37, 211, 113, 157, 167, 131, 181, 179, 269, 127, 421, 47, 523, 173, 331, 307, 149, 347, 257, 199, 277, 139, 151, 433, 223, 449, 227, 313, 647, 443, 283, 929, 509

Offset: 1

Author

Robert G. Wilson v, Jul 31 2017

Keywords

• nonn

Comments

Records: 3, 5, 13, 19, 43, 79, 89, 107, 239, 269, 421, 523, 647, 929, 1069, 1321, 1783, 1879, 2347, 4217, 4801, 7001, 7691, 9623, 22769, 23011, 27541, 29009, ..., .

Position of the n_th prime: 2, 1, 3, 5, 6, 4, 11, 7, 14, 17, 10, 31, 15, 8, 42, 22, 21, 27, 16, 12, 18, 9, ..., .

Prime index of a(n): 2, 1, 3, 6, 4, 5, 8, 14, 22, 11, 7, 20, 24, 9, 13, 19, 10, 21, 23, 28, 17, 16, 52, 26, 29, 51, ..., .

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A087898, A083771.

Programs

Mathematica

f[s_List] := Block[{p = Times @@ s, q = 2}, While[ MemberQ[s, q] || !PrimeQ[p*q - 1], q = NextPrime@ q]; Append[s, q]]; Nest[f, {3}, 40]

Formula

3*2*5*...*a(n) -1 is prime. a(n) is the least prime not previously in the sequence.