A235986 Numbers n such that two of the primes between n^2 and (n+1)^2 add up to n^2+(n+1)^2 - 1.
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60
Offset: 1
Keywords
Examples
For n=2 n+1=3; primes between 4 and 9 are (5,7);4+9-1=12 and 5+7=12. For n=3 n+1=4; primes between 9 and 16 are (11,13); 9+16-1=24 and 11+13=24. For n=18 n+1=19; primes between 324 and 361 are (331,337,347,349,353,359);324+361-1=684 and 331+353=684.
Programs
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Mathematica
ok[n_] := n>1 && Catch@Block[{p = NextPrime[n^2]}, While[p < (n+1)^2, If[PrimeQ[ 2*n*(n+1) - p], Throw@True, p = NextPrime@p]]; False]; Select[Range@100, ok] (* Giovanni Resta, Feb 26 2014 *) -
PARI
buildp(n) = {my(vp = []); forprime(p = n^2, (n+1)^2, vp = concat(vp, p);); vp;} issum(vp, n) = {my(summ = n^2+(n+1)^2 - 1); for (i = 1, #vp, for (j = i+1, #vp, if (vp[i]+vp[j] == summ, return (1)););); return (0);} isok(n) = my(vp = buildp(n)); issum(vp, n); \\ Michel Marcus, Jan 18 2014
Comments