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A262769 Integers k such that the concatenation of 2^k and k is prime. 1
3, 23, 63, 261, 281, 291, 4689, 11231, 12519 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

First three primes: 83, 838860823, 922337203685477580863.

a(10) > 120000. - Giovanni Resta, Apr 08 2016

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

For k = 23 we have 2^23 and 23 equal to 8388608 and 23, respectively, and 838860823 is a prime number.

MATHEMATICA

Select[Range@ 5000, PrimeQ[2^# * 10^IntegerLength[#] + #] &] (* Giovanni Resta, Apr 08 2016 *)

PROG

(Python)

from sympy import isprime

def afind(limit):

k, twok = 0, 1

while k <= limit:

if isprime(int(str(twok) + str(k))): print(k, end = ", ")

k, twok = k+1, twok*2

afind(2000) # Michael S. Branicky, Mar 23 2021

(PARI) isok(k) = isprime(eval(Str(2^k, k))); \\ Michel Marcus, Mar 23 2021

CROSSREFS

Cf. A000079.

Sequence in context: A196538 A216418 A254626 * A298393 A299511 A299311

Adjacent sequences: A262766 A262767 A262768 * A262770 A262771 A262772

KEYWORD

nonn,base,more

AUTHOR

Emre APARI, Mar 24 2016

EXTENSIONS

a(8)-a(9) from Giovanni Resta, Apr 08 2016

STATUS

approved

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Last modified November 28 05:56 EST 2022. Contains 358407 sequences. (Running on oeis4.)