A213739 Numbers n such that n and n^2 are sums of two successive primes.

12, 24, 42, 84, 90, 120, 204, 240, 372, 410, 456, 600, 630, 740, 762, 852, 882, 978, 1088, 1140, 1148, 1272, 1460, 1518, 1584, 1620, 1656, 1758, 1770, 1878, 1900, 1960, 2052, 2316, 2562, 2688, 2886, 2992, 3570, 3634, 3678, 3738, 3750, 3924, 4170, 4314, 4906

Offset

1,1

Comments

First terms not multiple of 6: 410, 740, 1088, 1148, 1460, 1900, 1960.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Zak Seidov, Table of n,p,q,n^2,r,s

Example

12=5+7, 144=71+73;
24=11+13, 576=283+293;
42=19+23, 1764=881+883.

Mathematica

Reap[ Do[ If[ (p=NextPrime[n/2, -1]; p+NextPrime[p] == n) && (q=NextPrime[n^2/2, -1]; q+NextPrime[q] == n^2) , Sow[n]], {n, 2, 5000, 2}]][[2, 1]] (* Jean-François Alcover, Jul 17 2012 *)

Prog

(PARI) p=2; forprime(q=3, 1e3, n=p+q; if(precprime(n^2/2)+nextprime((n^2+1)/2)==n^2, print1(n", ")); p=q) \\ Charles R Greathouse IV, Jun 21 2012

Crossrefs

Intersection of A001043 and A074924.

Sequence in context: A187975 A190566 A361856 * A102067 A181924 A367105

Adjacent sequences: A213736 A213737 A213738 * A213740 A213741 A213742

Keyword

nonn

Author

Zak Seidov, Jun 19 2012

Status

approved