A292743 Initial member of 6 consecutive primes a, b, c, d, e, f such that (a + f) = (b + e), (a + e) = (b + d) and (c + f) = (d + e).

6353, 14731, 19463, 71333, 77543, 78781, 83417, 104701, 105557, 130651, 185021, 202799, 214433, 218111, 344243, 351031, 357661, 358429, 380417, 408203, 443221, 466547, 496471, 505091, 587117, 593491, 634241, 652733, 702497, 746177, 778241, 807011, 886973, 949951

Offset: 1

Author

K. D. Bajpai, Sep 22 2017

Keywords

• nonn

Comments

None of the terms <= 10^7, is the smaller of twin primes.

78781 is the first term that is greater of twin primes; 78781 - 2 = 78779 is prime.

Examples

			6353 is a term because it is the initial member of 6 consecutive primes {6353, 6359, 6361, 6367, 6373, 6379} = {a, b, c, d, e, f}; and (a + f) = (b + e), (a + e) = (b + d) and (c + f) = (d + e).
		

Crossrefs

Cf. A000040, A292618, A292715.

Programs

Maple

A292743:= proc(n)local a,b,c,d,e,f; a:=ithprime(n); b:=ithprime(n+1); c:=ithprime(n+2); d:=ithprime(n+3); e:=ithprime(n+4); f:=ithprime(n+5);  if (a + f) = (b + e) and (a + e) = (b + d) and (c + f) = (d + e) then RETURN (ithprime(n)); fi; end: seq(A292743(n), n=1..100000);

Mathematica

Select[Partition[Prime@ Range[10^5], 6, 1], Function[{a, b, c, d, e, f}, And[(a + f) == (b + e), (a + e) == (b + d), (c + f) == (d + e)]] @@ # &][[All, 1]] (* Michael De Vlieger, Sep 22 2017 *)