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A318207
a(n) is the least prime p such that 2-adic valuation of p-3 is n.
1
2, 5, 7, 11, 19, 163, 67, 131, 1283, 6659, 25603, 10243, 4099, 57347, 114691, 32771, 65539, 3014659, 262147, 5767171, 5242883, 14680067, 71303171, 109051907, 218103811, 436207619, 335544323, 6308233219, 268435459, 9126805507, 1073741827, 130996502531, 21474836483, 403726925827, 85899345923
OFFSET
0,1
COMMENTS
For n >= 1, a(n) is the least prime p such that A007814(p-3) = n,
and the least k such that A023572(k) = n is A000720(a(n)).
By Dirichlet's theorem on primes in arithmetic progressions, a(n) exists for all n.
LINKS
EXAMPLE
a(3) = 11 because the highest power of 2 dividing 11-3=8 is 2^3, and 11 is the least prime with this property.
MAPLE
f:= proc(n) local k;
for k from 1 by 2 do
if isprime(k*2^n+3) then return k*2^n+3 fi
od
end proc:
f(0):= 2:
map(f, [$0..100]);
PROG
(PARI) a(n) = forprime(p=1, , if(valuation(p-3, 2)==n, return(p))) \\ Felix Fröhlich, Aug 23 2018
(Python)
from sympy import isprime
def A318207(n):
if n == 0: return 2
a = 1<<n
b = a<<1
while True:
if isprime(a+3):
return a+3
a += b # Chai Wah Wu, Jul 11 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Aug 21 2018
STATUS
approved