A131021 Prime semiperimeters of quadrilaterals with sides which are four consecutive primes.

13, 101, 739, 751, 1301, 1459, 1471, 1483, 1583, 1619, 1877, 1889, 1949, 2213, 2239, 2351, 2381, 2441, 2473, 2549, 2741, 2917, 3271, 3413, 3863, 4133, 4567, 4987, 5081, 5279, 5347, 5783, 5813, 6719, 7027, 7369, 7459, 7607, 8233, 8291, 9151, 9187, 9397

Offset: 1

Author

R. J. Mathar and Jonathan Vos Post, Jun 12 2007

Keywords

• easy
• nonn

Comments

These are the prime numbers in A131019(k), occurring at k=1, 13, 71, 72, 116, 127, 128, 129, 136, 138, 157, 158, 162, 183, 185, ....

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Programs

Maple

for n from 1 to 1000 do a131019 := add(ithprime(n+i),i=1..4)/2 : if isprime(a131019) then printf("%d, ",a131019) ; fi ; od:

Mathematica

Select[(Total /@ Partition[Prime[Range[10^3]], 4, 1])/2, PrimeQ] (* Zak Seidov, Nov 01 2012 *)

PARI

p=3;q=5;r=7;forprime(s=11,1e4,if(isprime(t=(p+q+r+s)/2),print1(t", ")); p=q; q=r; r=s) \\ Charles R Greathouse IV, Nov 01 2012

Formula

A131019 INTERSECT A000040.