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Search: id:A126193
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| A126193 |
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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. |
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2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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Eric Weisstein's World of Mathematics, Twin Prime Conjecture
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EXAMPLE
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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.
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PROGRAM
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(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 */
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CROSSREFS
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Cf. A001359, A126769, A126194.
Sequence in context: A068230 A040117 A145471 this_sequence A074965 A145475 A071695
Adjacent sequences: A126190 A126191 A126192 this_sequence A126194 A126195 A126196
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KEYWORD
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easy,nonn
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AUTHOR
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Tomas Xordan (xordan.tom(AT)gmail.com), Mar 07 2007
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EXTENSIONS
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Edited and checked by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 09 2007
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