A178953 -id:A178953 - cp's OEIS frontend

A178609 Largest k < n such that prime(n-k) + prime(n+k) = 2*prime(n).

0, 0, 1, 0, 3, 2, 2, 0, 0, 5, 3, 6, 4, 0, 0, 7, 7, 4, 8, 10, 0, 0, 7, 4, 11, 6, 2, 2, 0, 0, 13, 9, 10, 12, 0, 2, 16, 0, 6, 12, 13, 4, 19, 17, 15, 0, 18, 0, 0, 0, 11, 0, 0, 3, 1, 1, 0, 0, 6, 0, 0, 0, 27, 13, 0, 0, 17, 5, 29, 23, 26, 20, 26, 11, 7, 21, 20, 15, 19, 34, 21, 2, 21, 11, 10, 10, 10, 27, 3, 0, 0, 5, 32, 2, 0, 0, 0, 26, 0, 33

Offset: 1

Juri-Stepan Gerasimov, Dec 24 2010

The plot is very interesting.

			a(3)=1 because 5=prime(3)=(prime(3-1)+prime(3+1))/2=(3+7)/2.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A006562 (balanced primes), A178670 (number of k), A178698 (composite case), A179835 (smallest k).

a178609 n = head [k | k <- [n - 1, n - 2 .. 0], let p2 = 2 * a000040 n,
                      a000040 (n - k) + a000040 (n + k) == p2]
-- Reinhard Zumkeller, Jan 30 2014

Table[k=n-1; While[Prime[n-k]+Prime[n+k] != 2*Prime[n], k--]; k, {n,100}]

def A178609(n):
    return next(k for k in range(n)[::-1] if nth_prime(n-k)+nth_prime(n+k) == 2*nth_prime(n))
# D. S. McNeil, Dec 29 2010

a(A178953(n)) = 0.

Extended and corrected by T. D. Noe, Dec 28 2010

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

Original entry on oeis.org

2, 3, 7, 19, 23, 43, 47, 73, 79, 109, 113, 149, 163, 199, 223, 227, 229, 239, 241, 269, 271, 281, 283, 293, 313, 317, 463, 467, 499, 503, 509, 523, 619, 659, 661, 673, 677, 683, 691, 719, 829, 839, 859, 883, 887, 967, 1049, 1063, 1069, 1109, 1117, 1129, 1153, 1163, 1201

Offset: 1

Juri-Stepan Gerasimov, Jan 05 2011

nonn

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

R. K. Guy, Unsolved Problems in Number Theory, 3rd ed. Springer, 2004.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A000040, A100484, A006562, A178609, A178953, A178970.

Cf. A178670.

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:
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

From R. J. Mathar, Jan 05 2011: (Start)
{A000040(k): A178609(k)=0}.
a(n) = A000040(A178953(n)). (End)

cp's OEIS Frontend

A178609 Largest k < n such that prime(n-k) + prime(n+k) = 2*prime(n).

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