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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 (list; graph; refs; listen; history; text; internal format)
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

Robert Israel, Table of n, a(n) for n = 0..2000

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

Cf. A000720, A007814, A023572.

Sequence in context: A252282 A337497 A040122 * A038955 A172981 A141064

Adjacent sequences: A318204 A318205 A318206 * A318208 A318209 A318210

KEYWORD

nonn

AUTHOR

Robert Israel, Aug 21 2018

STATUS

approved

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Last modified March 21 15:50 EDT 2023. Contains 361408 sequences. (Running on oeis4.)