A054258 Concatenation of n in base 2 up to base 10 and n in base 10 down to base 2 is prime, all numbers are interpreted as decimals.

2607, 4007, 4069, 7597, 12411, 13583, 23041, 31113, 32619, 46187, 48469, 55777, 61411, 64387, 71143, 73837, 84761, 103559, 123797, 124043, 126613, 136509, 142019, 147449, 183981, 186889, 200183, 204219, 214819, 221101, 224123, 230977, 235493, 249049, 256489

Offset: 1

Author

Patrick De Geest, Feb 15 2000

Keywords

• nonn
• base

Examples

			a(1) = 2607 is a term since both 10100010111110120120220233404122002310413505735162607 and
  26073516505710413200234041222023310120120101000101111 are prime.
		

Links

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

Crossrefs

Intersection of A054256 and A054257.

Programs

Mathematica

Select[Range[250000],AllTrue[{FromDigits[Flatten[Table[IntegerDigits[#,b],{b,2,10}]]],FromDigits[ Flatten[Table[IntegerDigits[#,b],{b,10,2,-1}]]]},PrimeQ]&] (* Harvey P. Dale, May 28 2023 *)

Python

from gmpy2 import digits, is_prime
def ok(n): return is_prime(int("".join(digits(n, b) for b in list(range(2, 11))))) and is_prime(int("".join(digits(n, b) for b in list(range(10, 1, -1)))))
print([k for k in range(234567) if ok(k)]) # Michael S. Branicky, May 28 2023

Extensions

Offset changed to 1 and a(33) and beyond from Michael S. Branicky, May 28 2023