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

Author

Zak Seidov, Jun 19 2012

Keywords

• nonn

Comments

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

Examples

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

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

Crossrefs

Intersection of A001043 and A074924.

Programs

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 *)

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