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

5, 8, 10, 11, 15, 16, 17, 27, 36, 68, 69, 71, 111, 132, 189, 200, 212, 214, 234, 252, 262, 279, 317, 332, 343, 344, 364, 424, 426, 500, 506, 518, 520, 543, 563, 577, 606, 620, 658, 672, 696, 697, 737, 766, 882, 907, 982, 1009, 1064, 1087, 1089, 1091, 1162, 1164, 1172, 1226, 1256, 1268

Offset: 1

Author

Altug Alkan, Mar 18 2016

Keywords

• nonn

Comments

Integers k such that A006512(k) + A006512(k+3) = A006512(k+1) + A006512(k+2).

Integers k such that A014574(k) + A014574(k+3) = A014574(k+1) + A014574(k+2).

Examples

			5 is a term because A001359(5) = 29, A001359(6) = 41, A001359(7) = 59, A001359(8) = 71 and 29 + 71 = 41 + 59.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A006512, A014574, A053319.

Programs

Mathematica

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 *)

PARI

t(n, p=3) = { while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
b(n) = t(n) + t(n+3) - t(n+1) - t(n+2);
for(n=1, 2000, if(b(n) == 0, print1(n, ", ")));

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