A255274 - OEIS

%I #30 Nov 28 2024 11:16:40

%S 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,

%T 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,

%U 1,2,3,5,5,1,1,2,3,1,2,3,1,2,1,2,3,1,2

%N 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.

%C 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, ...

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

%H Michel Lagneau, <a href="/A255274/b255274.txt">Table of n, a(n) for n = 1..10000</a>

%H Jon Maiga, <a href="http://sequencedb.net/s/A255274">Computer-generated formulas for A255274</a>, Sequence Machine.

%F a(n) = n + (3-A020482(n+2))/2 = (A020481(n+2)-1)/2 via the Maiga link. - _Bill McEachen_, Jan 02 2022

%e 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.

%p 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:

%o (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

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

%K nonn

%O 1,4

%A _Michel Lagneau_, Feb 20 2015

%E Edited by _N. J. A. Sloane_, Sep 12 2017