A064102 Primes p = prime(k) such that prime(k) + prime(k+7) = prime(k+1) + prime(k+6) = prime(k+2) + prime(k+5) = prime(k+3) + prime(k+4).

17, 149, 677, 853, 1277, 5437, 6101, 13499, 13921, 19853, 22073, 41863, 49667, 51307, 51797, 55799, 61637, 66337, 83227, 91121, 100957, 103963, 109111, 113147, 128747, 136309, 137933, 148157, 158849, 163117, 167249, 179033, 205171, 208927

Offset: 1

Author

Robert G. Wilson v, Sep 17 2001

Keywords

• easy
• nonn

Examples

			17 + 43 = 19 + 41 = 23 + 37 = 29 + 31.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A000040, A022885, A064101, A359440.

Programs

Mathematica

a = {0, 0, 0, 0, 0, 0, 0, 0}; Do[ a = Delete[ a, 1 ]; a = Append[ a, Prime[ n ] ]; If[ a[ [ 1 ] ] + a[ [ 8 ] ] == a[ [ 2 ] ] + a[ [ 7 ] ] == a[ [ 3 ] ] + a[ [ 6 ] ] == a[ [ 4 ] ] + a[ [ 5 ] ], Print[ a[ [ 1 ] ] ] ], {n, 1, 10^4} ]
Select[Partition[Prime[Range[20000]],8,1],#[[1]]+#[[8]]==#[[2]]+#[[7]]==#[[3]]+#[[6]]==#[[4]]+#[[5]]&][[;;,1]] (* Harvey P. Dale, Jul 03 2025 *)

PARI

{ n=0; default(primelimit, 8300000); for (k=1, 10^9, p1=prime(k) + prime(k + 7); p2=prime(k + 1) + prime(k + 6); p3=prime(k + 2) + prime(k + 5); p4=prime(k + 3) + prime(k + 4); if (p1==p2 && p2==p3 && p3==p4, write("b064102.txt", n++, " ", prime(k)); if (n==400, break)) ) } \\ Harry J. Smith, Sep 07 2009

Formula

Primes p = prime(k) = A000040(k) such that A359440(k+3) >= 3. - Peter Munn, Jan 09 2023