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Search: id:A162652
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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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+0
14
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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
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7 = 1^2+1+5 = 3^2+3-5.
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MAPLE
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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
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Sequence in context: A074963 A110912 A085104 this_sequence A031158 A091431 A060800
Adjacent sequences: A162649 A162650 A162651 this_sequence A162653 A162654 A162655
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KEYWORD
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nonn,more
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AUTHOR
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Daniel Tisdale (daniel6874(AT)gmail.com), Jul 08 2009
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EXTENSIONS
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Definition revised by N. J. A. Sloane, Jul 17 2009
Corrected: 91 is not prime Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jul 18 2009
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009
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