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.

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

Table of n, a(n) for n=1..49.

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.

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

Author

Tomas Xordan, Mar 07 2007

Extensions

Edited and checked by Klaus Brockhaus, Mar 09 2007

Status

approved