A235806 Odd primes p with (p^2 - 1)/4 - prime((p - 1)/2) and (p^2 - 1)/4 - prime((p + 1)/2) both prime.
7, 11, 19, 29, 41, 43, 53, 59, 89, 109, 139, 179, 181, 229, 379, 401, 421, 431, 541, 587, 659, 811, 991, 1069, 1103, 1117, 1231, 1259, 1459, 1471, 1619, 1709, 1831, 1951, 2179, 2791, 2797, 2833, 2851, 3001, 3391, 3571, 3617, 3631, 3637, 3671, 3793, 3863, 3929, 3967
Offset: 1
Keywords
Examples
a(1) = 7 since neither (3^2-1)/4 - prime((3-1)/2) = 0 nor (5^2-1)/4 - prime((5+1)/2) = 1 is prime, but (7^2-1)/4 - prime((7-1)/2) = 12 - 5 = 7 and (7^2-1)/4 - prime((7+1)/2) = 12 - 7 = 5 are both prime.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
q[n_]:=PrimeQ[n(n+1)-Prime[n]]&&PrimeQ[n(n+1)-Prime[n+1]] n=0;Do[If[q[(Prime[k]-1)/2],n=n+1;Print[n," ",Prime[k]]],{k,2,1000}] Select[Prime[Range[2,600]],AllTrue[(#^2-1)/4-{Prime[(#-1)/2],Prime[ (#+1)/2]},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 05 2020 *)
Comments