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A162652
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Primes p such that there are positive integers m and n and a prime q such that p = m^2+m-q = n^2+n+q.
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12
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7, 13, 31, 43, 73, 211, 241, 421, 463, 1123, 1723, 2551, 2971, 4831, 5701, 6163, 8011, 8191, 9901, 11131, 12433, 14281, 17293, 19183, 20023, 23563, 24181, 28393, 30103, 31153, 35911, 37831, 43891, 46441, 53593, 60271, 77563, 83233, 86143, 95791
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| To test if a prime p is a member, p = n^2+n+q gives a finite list of possible pairs (n,q), and, for each value of q, m^2+m=p+q determines a putative value of m. - N. J. A. Sloane, Jul 17 2009
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EXAMPLE
| 7 = 1^2+1+5 = 3^2+3-5.
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MAPLE
| isA002378 := proc(n) if n >= 0 then if issqr(4*n+1) then RETURN(type( sqrt(4*n+1), 'odd')) ; else false; fi; else false; fi; end: # primes p such there is a prime q<p such that # p+q and p-q are both oblong numbers. isA162652 := proc(p) local j, q; if isprime(p) then for j from 1 do q := ithprime(j) ; if q >= p then break; fi; if isA002378(p+q) and isA002378(p-q) then RETURN(true) ; fi; od: false ; else false; fi; end: for n from 1 to 4000 do if isA162652(ithprime(n)) then printf("%d, ", ithprime(n)) ; fi; od; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]
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CROSSREFS
| Cf. A163418. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2010]
Sequence in context: A074963 A110912 A085104 * A181141 A031158 A091431
Adjacent sequences: A162649 A162650 A162651 * A162653 A162654 A162655
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KEYWORD
| nonn
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AUTHOR
| Daniel Tisdale (daniel6874(AT)gmail.com), Jul 08 2009
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EXTENSIONS
| Definition revised by N. J. A. Sloane, Jul 17 2009
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009
Extended beyond a(31) by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2010
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