A210957 -id:A210957 - cp's OEIS frontend

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

Michel Lagneau, Feb 20 2015

nonn

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).

			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.

Michel Lagneau, Table of n, a(n) for n = 1..10000
Jon Maiga, Computer-generated formulas for A255274, Sequence Machine.

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

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:

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

a(n) = n + (3-A020482(n+2))/2 = (A020481(n+2)-1)/2 via the Maiga link. - Bill McEachen, Jan 02 2022

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

cp's OEIS Frontend

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.

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