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A236512 Primes whose representation in base (2), base (3), base (4) and base (5) are also prime when read in decimal. 2
9241, 85303, 110581, 296011, 331081, 465523, 644353, 659371, 849943, 1108993, 1116163, 1210483, 2149471, 2469241, 2963923, 3409753, 3704203, 4451071, 4774801, 4978003, 5665213, 5674993, 5995021, 6507343, 6817501, 7529941, 7596373, 7693531, 7973653, 8320831, 8344681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..797

EXAMPLE

9241 is in the sequence because it is prime. Its representation in base (2):{10010000011001}, base (3):{110200021}, base (4):{2100121} and base (5):{243431}, when read in decimal are also prime.

MATHEMATICA

t={}; n=1; While[Length[t]<100, n=NextPrime[n]; If[PrimeQ[FromDigits[IntegerDigits[n, 2]]]&&PrimeQ[FromDigits[IntegerDigits[n, 3]]] &&PrimeQ[FromDigits[IntegerDigits[n, 4]]]&&PrimeQ[FromDigits[IntegerDigits[n, 5]]], ApendTo[t, n]]] t (*K. D. Bajpai*)

PROG

(PARI)

default(primelimit, 2^31)

base_b(n, b) = {

my(s=[], r, x=10);

while(n>0,

r = n%b;

n = n\b;

s = concat(r, s)

);

eval(Pol(s))

}

A236512(maxp) = {

forprime(p=2, maxp,

if(isprime(base_b(p, 2)) &&

isprime(base_b(p, 3)) &&

isprime(base_b(p, 4)) &&

isprime(base_b(p, 5)), print1(p, ", ")

)

)

}

\\ Colin Barker, Jan 29 2014

CROSSREFS

Cf. A000040 (prime numbers), A065720 (primes: binary representation is also prime),

A236365 (primes: binary and octal representation is also prime).

Sequence in context: A272596 A189984 A092005 * A031848 A184211 A035910

Adjacent sequences: A236509 A236510 A236511 * A236513 A236514 A236515

KEYWORD

nonn,base

AUTHOR

K. D. Bajpai, Jan 27 2014

STATUS

approved

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Last modified January 31 01:17 EST 2023. Contains 359947 sequences. (Running on oeis4.)