A022884 Numbers k such that prime(k) + prime(k+3) = prime(k+1) + prime(k+2).

3, 4, 5, 6, 9, 12, 16, 21, 25, 26, 27, 29, 33, 37, 41, 43, 48, 54, 56, 63, 71, 74, 77, 80, 81, 84, 88, 92, 93, 100, 103, 105, 108, 124, 125, 126, 134, 140, 142, 147, 149, 151, 153, 156, 165, 171, 175, 176, 181, 185, 191, 200, 208, 211, 216, 224, 234, 235

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Examples

			The ninth prime is 23. We verify that 23 + 37 = 60 = 29 + 31. Hence 9 is in the sequence.
The tenth prime is 29. We see that 29 + 41 = 70 but 31 + 37 = 68, so 10 is not in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Crossrefs

Cf. A000720, A022885

Cf. A261470. - Altug Alkan, Oct 28 2015

Programs

Magma

[n: n in [1..250] |(NthPrime(n)+NthPrime(n+3)) eq (NthPrime(n+1)+ NthPrime(n+2))]; // Vincenzo Librandi, Nov 04 2018

Mathematica

Select[Range@ 240, Prime[#] + Prime[# + 3] == Prime[# + 1] + Prime[# + 2] &] (* Michael De Vlieger, Oct 28 2015 *)

PARI

isok(k) = prime(k+3)+prime(k) == prime(k+1)+prime(k+2); \\ Michel Marcus, Aug 20 2015

PARI

is(n,p=prime(n))=my(q=nextprime(p+1),r=nextprime(q+1),s=nextprime(r+1)); p+s==q+r
n=0; forprime(p=2,1e5, if(is(n++,p), print1(n", "))) \\ Charles R Greathouse IV, Oct 28 2015

Formula

a(n) = A000720(A022885(n)). - Zak Seidov, Oct 23 2015

Extensions

Name edited by Michel Marcus, Aug 20 2015