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

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

1,1

Comments

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

References

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

Links

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

Formula

From R. J. Mathar, Jan 05 2011: (Start)

{A000040(k): A178609(k)=0}.

a(n) = A000040(A178953(n)). (End)

Maple

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

Crossrefs

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

Cf. A178670.

Sequence in context: A352538 A117763 A165571 * A138111 A218100 A349622

Adjacent sequences: A178951 A178952 A178953 * A178955 A178956 A178957

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 05 2011

Status

approved