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%I #10 Mar 20 2016 12:59:04
%S 5,8,10,11,15,16,17,27,36,68,69,71,111,132,189,200,212,214,234,252,
%T 262,279,317,332,343,344,364,424,426,500,506,518,520,543,563,577,606,
%U 620,658,672,696,697,737,766,882,907,982,1009,1064,1087,1089,1091,1162,1164,1172,1226,1256,1268
%N Integers n such that A001359(n) + A001359(n+3) = A001359(n+1) + A001359(n+2).
%C Integers n such that A006512(n) + A006512(n+3) = A006512(n+1) + A006512(n+2).
%C Integers n such that A014574(n) + A014574(n+3) = A014574(n+1) + A014574(n+2).
%e 5 is a term because A001359(5) = 29, A001359(6) = 41, A001359(7) = 59, A001359(8) = 71 and 29 + 71 = 41 + 59.
%t s = Select[Prime@ Range[10^6], PrimeQ[# + 2] &]; Select[Range@ 1300, s[[#]] + s[[# + 3]] == s[[# + 1]] + s[[# + 2]] &] (* after _Robert G. Wilson v_ at A001359 *)
%o (PARI) t(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
%o b(n) = t(n) + t(n+3) - t(n+1) - t(n+2);
%o for(n=1, 2000, if(b(n) == 0, print1(n, ", ")));
%Y Cf. A001359, A006512, A014574, A053319.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 18 2016
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