A235859 Define a(4)=3, then a(n+1) is the smallest prime P such that a(n) <= P < 2*n with 2*n-P=Q prime and, if not possible, a(n+1) is the smallest prime P such that P < a(n) < 2*n with 2*n-P=Q prime.
3, 3, 5, 11, 11, 11, 13, 17, 17, 19, 23, 23, 29, 29, 29, 31, 37, 37, 37, 41, 41, 43, 47, 47, 53, 53, 53, 59, 59, 59, 61, 67, 67, 67, 71, 71, 73, 79, 79, 79, 83, 83, 89, 89, 89, 19, 29, 29, 31, 47, 47, 67, 71, 71, 73, 89, 89, 103, 107, 107, 109, 113, 113
Offset: 4
Examples
a(4)=3 as 2*4-3=5 prime by definition a(5)=3 as 2*5-3=7 prime, a(5)=a(4), a(5)<5 a(6)=5 as 2*6-5=7 prime, a(6)>a(5), a(6)<6 a(7)=5 not possible as 14-5=9 composite a(7)=7 not possible as 7=7 a(7)=11 as 2*7-11=3 prime ......................... a(48)=89 as 2*48-89=7 prime a(49)=89 not possible as 2*49-89=9 composite a(49)=97 not possible as 2*49-97=unity a(49)=19 as 19 is the smallest prime such that 2*49-19 is prime a(50)=29 as 29 is the smallest prime >=19 such that 2*50-29 is prime
Links
- Pierre CAMI, Table of n, a(n) for n = 4..10005