A215895 Primes p with property that there exists a number D such that p-3D, p-2D, p-D, p+D, p+2D, p+3D are all primes.
457, 677, 809, 829, 1039, 1249, 1453, 1459, 1511, 1721, 2083, 2879, 3203, 3499, 3527, 3581, 3919, 4129, 4139, 4157, 4273, 4339, 4549, 5519, 5689, 5711, 5843, 6143, 6329, 6359, 6619, 6803, 6949, 7001, 7013, 7103, 7109, 7211, 7393, 7459, 7477, 7481, 7549, 7673, 7723, 7789
Offset: 1
Keywords
Examples
457 is in the sequence because with D=150: 7, 157, 307, 607, 757, 907 are all primes.
Links
- Alois P. Heinz and Lei Zhou, Table of n, a(n) for n = 1..10000 (terms n = 1..2000 from Alois P. Heinz)
Crossrefs
Cf. A215642.
Programs
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Maple
a:= proc(n) option remember; local D, p; p:= `if`(n=1, 1, a(n-1)); do p:= nextprime(p); for D to iquo(p, 3) do if nops(select(isprime, {(p-k*D)$k=-3..3}))=7 then return p fi od od end: seq (a(n), n=1..40); # Alois P. Heinz, Aug 26 2012 -
Mathematica
a[n_] := a[n] = Module[{D, p}, p = If[n==1, 1, a[n-1]]; While[True, p = NextPrime[p]; For[D = 1, D <= Quotient[p, 3], D++, If[AllTrue[p - Range[-3, 3] D, PrimeQ], Return [p]]]]]; Array[a, 40] (* Jean-François Alcover, Nov 13 2020, after Alois P. Heinz *)
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