A235920 Primes p with prime(p) - p + 1 and (p^2 - 1)/4 - prime(p) both prime.
17, 31, 41, 43, 61, 71, 83, 103, 109, 173, 181, 211, 271, 349, 353, 541, 661, 673, 743, 811, 911, 953, 971, 1171, 1429, 1471, 1483, 1723, 1787, 2053, 2203, 2579, 2749, 3019, 3299, 3391, 3433, 3463, 3727, 3917, 4003, 4021, 4049, 4243, 4447, 4567, 4657, 4729, 4801, 4993
Offset: 1
Keywords
Examples
a(1) = 17 with prime(17) - 17 + 1 = 59 - 16 = 43 and (17^2 - 1)/4 - prime(17) = 72 - 59 = 13 both prime.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
PQ[n_]:=n>0&&PrimeQ[n] p[n_]:=PrimeQ[Prime[n]-n+1]&&PQ[(n^2-1)/4-Prime[n]] n=0;Do[If[p[Prime[k]],n=n+1;Print[n," ",Prime[k]]],{k,1,1000}]
Comments