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 A162652 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. 13
 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; text; internal format)
 OFFSET 1,1 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 Also, primes of the form (p^2+3)/4 with p odd prime. - Zak Seidov, May 10 2014 LINKS Jean-François Alcover, Table of n, a(n) for n = 1..77 EXAMPLE 7 = 1^2+1+5 = 3^2+3-5. 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 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; # R. J. Mathar, Jul 17 2009 MATHEMATICA sol[p_] := m^2 + m - p /. Solve[m>0 && n>0 && 2p == m + m^2 + n + n^2, {m, n}, Integers]; Reap[For[p = 2, p < 10^6, p = NextPrime[p], qsel = Select[sol[p], PrimeQ]; If[qsel != {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Mar 25 2020 *) CROSSREFS Cf. A163418. - R. J. Mathar, Feb 05 2010 Sequence in context: A308851 A298027 A085104 * A306889 A181141 A031158 Adjacent sequences:  A162649 A162650 A162651 * A162653 A162654 A162655 KEYWORD nonn AUTHOR Daniel Tisdale, Jul 08 2009 EXTENSIONS Definition revised by N. J. A. Sloane, Jul 17 2009 More terms from R. J. Mathar, Jul 17 2009 Extended beyond a(31) by R. J. Mathar, Feb 05 2010 STATUS approved

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Last modified January 16 13:35 EST 2022. Contains 350376 sequences. (Running on oeis4.)