A188268 Smallest k such that prime(k) + prime(k+1) = prime(k+2) + prime(k-n).

4, 8, 153, 61, 258, 649, 4134, 3384, 29295, 101468, 33607, 165325, 298594, 703923, 2393291, 32214330, 12432950, 12849377, 539169143, 396264119, 406027081, 33772761, 5097974305, 4764006510, 23719367863, 44982489668, 54393474823, 25708849510

Offset: 1

Author

Michel Lagneau, Mar 30 2011

Keywords

• nonn

Comments

Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: every even integer greater than 2 can be expressed as the sum of two primes. Because there exist several decompositions (see A002375), this sequence gives k for a second decomposition of prime(k) + prime(k+1) that gives prime(k+2) + prime(k-n).

a(n) > pi(2*10^12) for n >= 29. - Donovan Johnson, Apr 06 2011

Examples

			a(2) = 8 because prime(8) + prime(9) = prime(10) + prime(6); i.e., 19 + 23 = 29 + 13.
		

Crossrefs

Cf. A001031, A045917, A002375, A045917.

Programs

Maple

A188268 := proc(n) local k ,pk; k := 1+n ; pk := Array([ithprime(k), ithprime(k+1), ithprime(k+2), ithprime(k-n)]) ; for k from 1+n do if pk[1]+pk[2]-pk[3] = pk[4] then return k ; end if; pk[1] := pk[2] ; pk[2] := pk[3] ; pk[3] := nextprime(pk[2]) ; pk[4] := nextprime(pk[4]) ; end do; end proc: # R. J. Mathar, Mar 31 2011

Extensions

a(23)-a(28) from Donovan Johnson, Apr 06 2011