A185956 Fajtlowicz q-primes.

2, 3, 5, 7, 13, 11, 19, 17, 29, 23, 37, 43, 31, 47, 41, 61, 53, 67, 71, 59, 73, 89, 79, 83, 103, 101, 107, 109, 97, 127, 131, 113, 139, 137, 151, 157, 149, 163, 173, 181, 191, 167, 193, 211, 179, 199, 223, 197, 227, 233, 239, 229, 241, 257, 251, 277, 293, 283, 313, 281, 271, 307, 269, 337, 263, 311, 347, 317, 359, 353, 367, 331, 373, 379, 349, 389, 383, 401, 397, 421, 409, 443, 431, 419, 449, 433, 439, 467, 457, 463, 491, 487, 479

Offset

1,1

Comments

S. Fajtlowicz defined two related sequences of primes, p(n) and q(n), as follows:

1. q(1)=2 and p(1)=7.

2. q(n+1) is the smallest prime dividing p(n)+2.

3. p(n+1) is the smallest prime p larger than p(n) such that p+2 is not prime and not divisible by any of q(1),q(2),...,q(n+1).

Paul Erdős and C. Larson conjecture that all primes occur in the sequence of q's.

The values of p and q were computed by Bethany Turner.

References

Siemion Fajtlowicz, Written on the Wall: Conjectures of Graffiti, #784 (1994).

Links

Amiram Eldar, Table of n, a(n) for n = 1..500 (terms 1..218 from R. J. Mathar)

Siemion Fajtlowicz, Graffity & automated conjecture making (2009), click on "conjectures up to No. 894", see page 136.

Maple

A185956 := proc(n)
    option remember;
    if n = 1 then
        2;
    else
        A020639(2+A185955(n-1)) ;
    end if;
end proc:
seq(A185956(n), n=1..20) ; # R. J. Mathar, Jul 28 2019

Mathematica

lpf[n_] := FactorInteger[n][[1, 1]]; q[1] = 2; p[1] = 7; q[n_] := q[n] = lpf[p[n - 1] + 2]; p[n_] := Module[{pn = NextPrime[p[n - 1]]}, While[PrimeQ[pn + 2] || AnyTrue[Array[q, n], Divisible[pn + 2, #] &], pn = NextPrime[pn]]; pn]; Array[q, 50] (* Amiram Eldar, Apr 23 2021 *)

Crossrefs

Cf. A185955.

Sequence in context: A065107 A338944 A351528 * A316885 A225039 A264731

Adjacent sequences: A185953 A185954 A185955 * A185957 A185958 A185959

Keyword

nonn

Author

Craig Eric Larson, Feb 07 2011

Status

approved