A126193 Lesser of twin primes (A001359) of the form p = k^2+s such that q = k^4+s is also a lesser of twin primes, q > p and s >= 0.
5, 17, 29, 41, 59, 71, 107, 137, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607, 1619, 1667, 1697, 1721
Offset: 1
Examples
5 = 2^2+1 and 17 = 2^4+1; 5 and 17 are lesser of twin primes; 41 = 4^2+25 and 281 = 4^4+25; 41 and 281 are lesser of twin primes.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Eric Weisstein's World of Mathematics, Twin Prime Conjecture
Programs
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Maple
filter:= proc(p) local s,k; if not(isprime(p) and isprime(p+2)) then return false fi; for k from 2 do s:= p - k^2; if s < 0 then return false fi; if isprime(s+k^4) and isprime(s+k^4+2) then return true fi; od end proc: select(filter, [seq(i,i=5..2000, 6)]); # Robert Israel, Sep 15 2024 -
PARI
{m=42; v=[]; for(k=2, m, for(s=1, (m+1)^2-1, if((p=k^2+s)
Extensions
Edited and checked by Klaus Brockhaus, Mar 09 2007
Definition corrected by Robert Israel, Sep 15 2024
Comments