A235743 Primes p(k) such that p(k) + p(k+3) = p(k+1) + p(k+2) + 4.

17, 41, 79, 131, 149, 173, 227, 233, 239, 347, 349, 379, 439, 463, 521, 599, 641, 673, 677, 983, 1013, 1091, 1231, 1277, 1427, 1429, 1453, 1487, 1549, 1607, 1811, 1949, 2099, 2203, 2309, 2579, 2609, 2687, 2689, 2833, 2857, 2903, 2909, 2917, 3083, 3167, 3299

Offset: 1

Author

Vladimir Shevelev, Jan 15 2014

Keywords

• nonn

Comments

If p(k) is in the sequence, then the four consecutive primes p(k), p(k+1), p(k+2), p(k+3) possess a property of quadruplet of consecutive squares: n^2 + (n+3)^2 = (n+1)^2 + (n+2)^2 + 4.

Cf. A022885, where such quadruplets possess a linear property: n + (n+3) = (n+1) + (n+2).

Examples

			17 is in the sequence since 17, 19, 23, and 29 are four consecutive primes and it holds 17 + 29 = 19 + 23 + 4.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A022885.

Programs

Mathematica

f[{a_,b_,c_,d_}]:= a-b-c+d; First /@ Select[Partition[Prime@ Range@ 500, 4, 1], f@# == 4 &] (* Giovanni Resta, Jan 16 2014 *)
Transpose[Select[Partition[Prime[Range[5000]], 4, 1], First[#] + Last[#]==#[[2]] + #[[3]] + 4&]][[1]] (* Vincenzo Librandi, Feb 02 2014 *)

PARI

isok(p) = { my(k = primepi(p)); (p == prime(k)) && ((prime(k) + prime(k+3)) == (prime(k+1) + prime(k+2) + 4));} \\ Michel Marcus, Jan 15 2014

Extensions

More terms from Michel Marcus, Jan 15 2014