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A178954 Primes prime(j) which cannot be written as 2*prime(j) = prime(j+k) + prime(j-k) for any 0 < k < j.

%I A178954 #25 Jan 06 2019 04:06:47
%S A178954 2,3,7,19,23,43,47,73,79,109,113,149,163,199,223,227,229,239,241,269,
%T A178954 271,281,283,293,313,317,463,467,499,503,509,523,619,659,661,673,677,
%U A178954 683,691,719,829,839,859,883,887,967,1049,1063,1069,1109,1117,1129,1153,1163,1201
%N A178954 Primes prime(j) which cannot be written as 2*prime(j) = prime(j+k) + prime(j-k) for any 0 < k < j.
%C A178954 Sequence A127925, in which 2*prime(j) < prime(j+k) + prime(j-k) for all 0 < k < j, is a subsequence of this sequence.  According to section A14 of Guy, Pomerance proved that A127925 is an infinite sequence. Hence, this sequence is also infinite. - _T. D. Noe_, Jan 10 2011
%D A178954 R. K. Guy, Unsolved Problems in Number Theory, 3rd ed. Springer, 2004.
%H A178954 T. D. Noe, <a href="/A178954/b178954.txt">Table of n, a(n) for n = 1..1000</a>
%F A178954 From _R. J. Mathar_, Jan 05 2011: (Start)
%F A178954 {A000040(k): A178609(k)=0}.
%F A178954 a(n) = A000040(A178953(n)). (End)
%p A178954 A178609 := proc(n) for k from n-1 to 0 by -1 do if ithprime(n-k)+ithprime(n+k)=2*ithprime(n) then return k; end if; end do: end proc:
%p A178954 for n from 1 to 200 do if A178609(n) = 0 then printf("%d,",ithprime(n)) ; end if; end do: # _R. J. Mathar_, Jan 05 2011
%Y A178954 Cf. A000040, A100484, A006562, A178609, A178953, A178970.
%Y A178954 Cf. A178670.
%K A178954 nonn
%O A178954 1,1
%A A178954 _Juri-Stepan Gerasimov_, Jan 05 2011