A360147 Primes in base 10 that are also prime when read in a smaller base that is one plus the largest digit in the prime in base 10.

2, 3, 5, 7, 11, 13, 23, 31, 37, 43, 61, 73, 101, 103, 107, 113, 131, 151, 223, 227, 233, 241, 251, 277, 307, 311, 331, 337, 373, 401, 461, 463, 467, 521, 547, 557, 577, 661, 673, 701, 827, 887, 1013, 1033, 1103, 1151, 1181, 1213, 1223, 1231, 1301, 1327, 1567

Offset: 1

Author

Alfred Jacob Mohan, Jan 27 2023

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A038617.

Programs

Maple

q:= n-> isprime(n) and (l-> (d-> d<9 and isprime(add(l[i]*
   (d+1)^(i-1), i=1..nops(l))))(max(l)))(convert(n, base, 10)):
select(q, [$1..2000])[];  # Alois P. Heinz, Jan 27 2023

Mathematica

q[p_] := Module[{d = IntegerDigits[p], b}, b = Max[d] + 1; b <= 9 && PrimeQ[FromDigits[d, b]]]; Select[Prime[Range[250]], q] (* Amiram Eldar, Jan 27 2023 *)

PARI

isok(p)=if(isprime(p), my(v=digits(p), b=vecmax(v)+1); b<10 && isprime(fromdigits(v,b)), 0) \\ Andrew Howroyd, Jan 27 2023

Python

from sympy import isprime
def ok(n):
    if not isprime(n): return False
    s = str(n)
    b = int(max(s)) + 1
    return b != 10 and isprime(int(s, b))
print([k for k in range(1600) if ok(k)]) # Michael S. Branicky, Jan 27 2023

Extensions

More terms from Michael S. Branicky, Jan 27 2023