A364456 - OEIS

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A364456

Lexicographically earliest sequence of distinct primes such that a(1)*a(2)*...*a(n-1) - a(n) is prime for n>=1 with a(1)=5.

5, 2, 3, 7, 11, 13, 17, 29, 23, 31, 37, 73, 41, 19, 59, 89, 83, 43, 47, 71, 79, 151, 137, 67, 181, 163, 167, 101, 103, 97, 53, 223, 61, 227, 229, 113, 109, 191, 127, 157, 389, 349, 199, 337, 463, 577, 193, 149, 991, 107, 139, 233, 131, 691, 173, 557, 307, 461, 313, 619, 353, 281, 487, 947, 641, 283, 673, 271, 433, 263

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OFFSET

1,1

COMMENTS

Conjecture: This sequence contains all primes.

Conjecture: If f(n) = a(1)*a(2)*...*a(n-1) then f(n)-a(n) is the previous prime of f(n) - 1 for n > 1.

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

a(4) = 7 because 7 is the least prime not already in the sequence such that 5*2*3 - 7 = 30 - 7 = 23 which is prime.

MATHEMATICA

a[1]=5; a[n_]:=a[n]=(k=2; While[MemberQ[s=Array[a, n-1], k]||!PrimeQ[Times@@s-k], k=NextPrime@k]; k); Array[a, 70]