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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).

%I A064102 #15 Jul 03 2025 17:31:05
%S A064102 17,149,677,853,1277,5437,6101,13499,13921,19853,22073,41863,49667,
%T A064102 51307,51797,55799,61637,66337,83227,91121,100957,103963,109111,
%U A064102 113147,128747,136309,137933,148157,158849,163117,167249,179033,205171,208927
%N 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).
%H A064102 Harry J. Smith, <a href="/A064102/b064102.txt">Table of n, a(n) for n = 1..400</a>
%F A064102 Primes p = prime(k) = A000040(k) such that A359440(k+3) >= 3. - _Peter Munn_, Jan 09 2023
%e A064102 17 + 43 = 19 + 41 = 23 + 37 = 29 + 31.
%t A064102 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} ]
%t A064102 Select[Partition[Prime[Range[20000]],8,1],#[[1]]+#[[8]]==#[[2]]+#[[7]]==#[[3]]+#[[6]]==#[[4]]+#[[5]]&][[;;,1]] (* _Harvey P. Dale_, Jul 03 2025 *)
%o A064102 (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
%Y A064102 Cf. A000040, A022885, A064101, A359440.
%K A064102 easy,nonn
%O A064102 1,1
%A A064102 _Robert G. Wilson v_, Sep 17 2001