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A270535 Integers k such that A001359(k) + A001359(k+3) = A001359(k+1) + A001359(k+2).

%I A270535 #17 Feb 23 2025 02:41:16
%S A270535 5,8,10,11,15,16,17,27,36,68,69,71,111,132,189,200,212,214,234,252,
%T A270535 262,279,317,332,343,344,364,424,426,500,506,518,520,543,563,577,606,
%U A270535 620,658,672,696,697,737,766,882,907,982,1009,1064,1087,1089,1091,1162,1164,1172,1226,1256,1268
%N A270535 Integers k such that A001359(k) + A001359(k+3) = A001359(k+1) + A001359(k+2).
%C A270535 Integers k such that A006512(k) + A006512(k+3) = A006512(k+1) + A006512(k+2).
%C A270535 Integers k such that A014574(k) + A014574(k+3) = A014574(k+1) + A014574(k+2).
%H A270535 Amiram Eldar, <a href="/A270535/b270535.txt">Table of n, a(n) for n = 1..10000</a>
%e A270535 5 is a term because A001359(5) = 29, A001359(6) = 41, A001359(7) = 59, A001359(8) = 71 and 29 + 71 = 41 + 59.
%t A270535 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 A270535 (PARI) t(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
%o A270535 b(n) = t(n) + t(n+3) - t(n+1) - t(n+2);
%o A270535 for(n=1, 2000, if(b(n) == 0, print1(n, ", ")));
%o A270535 (PARI) list(lim) = {my(k = 0, p1 = 2, t = [0, 0, 0, 0]); forprime(p2 = 3, lim, if(p2 - p1 == 2, k++; t = concat(t[2..4], p1); if(t[1] + t[4] == t[2] + t[3], print1(k-3, ", "))); p1 = p2);} \\ _Amiram Eldar_, Feb 22 2025
%Y A270535 Cf. A001359, A006512, A014574, A053319.
%K A270535 nonn
%O A270535 1,1
%A A270535 _Altug Alkan_, Mar 18 2016