A057777 a(n) is the smallest number such that a(n)+1 is a prime and the largest power of 2 which divides it is 2^n.
1, 2, 4, 40, 16, 96, 192, 640, 256, 7680, 13312, 18432, 12288, 40960, 114688, 163840, 65536, 1179648, 786432, 5767168, 7340032, 23068672, 104857600, 377487360, 754974720, 167772160, 469762048, 2013265920, 3489660928, 12348030976, 3221225472, 75161927680, 184683593728
Offset: 0
Keywords
Examples
The 4th term is 40. It is divisible by 8, 40+1 = 41 is prime. Smaller multiples of 8 are not suitable because, e.g., albeit 8|16 and 16+1 = 17 is a prime, but the largest power of 2 that divides 16 is not 8, it is 16. So 16 is not the 3rd, it is the 4th term here.
Links
- Amiram Eldar, Table of n, a(n) for n = 0..1000
Formula
a(n) = A057775(n) - 1. - Sean A. Irvine, Jun 27 2022
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), Nov 03 2000