A255274 From Goldbach conjecture: Consider the pairs (2n-+1, 3), (2n-1, 5), (2n-3, 7), ..., (3, 2n+1) of odd numbers having sum 2n+4; a(n) is the index of the first pair of primes (p, q) on the list.

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 9, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 6, 5, 6, 9, 1, 2, 1, 2, 3, 1, 1, 2, 3, 5, 5, 1, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2

Offset

1,4

Comments

a(n) = A049847(n) for n = 1..46. The values of n such that a(n) is different from A049847(n) are 47, 59, 62, 72, 93, 102, 108, 123, 144, 149, 152, 161, 164, 171, 182, 197, 203, 207, 213, 227, ...

The corresponding pairs of primes are (3, 3), (3, 5), (3, 7), (5, 7), (3, 11), (3, 13), (5, 13), (3, 17), ... (A210957).

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Jon Maiga, Computer-generated formulas for A255274, Sequence Machine.

Formula

a(n) = n + (3-A020482(n+2))/2 = (A020481(n+2)-1)/2. - Bill McEachen, Jan 02 2022 [Should these formulas be credited to Jon Maiga? - N. J. A. Sloane, Feb 06 2022]

Example

a(13)=3 because 2*13 + 4 = 30 => 13 pairs (27,3), (25,5), (23,7), ..., (3,27) and the pair (23,7) is the third pair having prime elements.

Maple

nn:=100:for n from 6 by 2 to nn do:ii:=0:it:=1:for p from 3 by 2 to n while(ii=0) do:if type(n-p, prime)=true and type(p, prime)=true then ii:=1: printf(`%d, `, it):else it:=it+1:fi:od:od:

Prog

(PARI) a(n)=my(m=2*n+4); forprime(q=3, n+2, if(isprime(m-q), return(q\2))) \\ Charles R Greathouse IV, Jan 07 2022

Crossrefs

Cf. A000040, A002375, A049847, A210957, A020482.

Sequence in context: A091304 A340101 A049847 * A025431 A161070 A161109

Adjacent sequences: A255271 A255272 A255273 * A255275 A255276 A255277

Keyword

nonn

Author

Michel Lagneau, Feb 20 2015

Extensions

Edited by N. J. A. Sloane, Sep 12 2017

Status

approved