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

1,1

Comments

p = q-k^4+k^2 where p and q are lesser of twin primes and p < q.

May be connected with the twin prime conjecture (see link).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Prime Conjecture

Example

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.

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

Prog

(PARI) {m=42; v=[]; for(k=2, m, for(s=1, (m+1)^2-1, if((p=k^2+s)<m^2&&isprime(p)&&isprime(p+2)&&(q=k^4+s)>p&&isprime(q)&&isprime(q+2), v=concat(v, p)))); v=listsort(List(v), 1); for(j=1, #v, print1(v[j], ", "))} /* Klaus Brockhaus, Mar 09 2007 */

Crossrefs

Cf. A001359, A126769, A126194.

Sequence in context: A068230 A040117 A145471 * A074965 A145475 A071695

Adjacent sequences: A126190 A126191 A126192 * A126194 A126195 A126196

Keyword

easy,nonn,changed

Author

Tomas Xordan, Mar 07 2007

Extensions

Edited and checked by Klaus Brockhaus, Mar 09 2007

Definition corrected by Robert Israel, Sep 15 2024

Status

approved