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A213739
Numbers n such that n and n^2 are sums of two successive primes.
2
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
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 * A377590 A102067 A181924
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 19 2012
STATUS
approved