A255073 Primes that remain prime after each digit is replaced by the power of its position.

2, 3, 5, 7, 11, 13, 17, 19, 23, 37, 43, 47, 67, 71, 79, 83, 101, 103, 107, 109, 113, 131, 137, 139, 167, 173, 179, 191, 211, 241, 263, 269, 281, 307, 311, 313, 331, 337, 353, 359, 367, 397, 431, 479, 491, 503, 521, 577, 593, 601, 613, 617, 659, 673

Offset: 1

Author

Abhiram R Devesh, Feb 14 2015

Keywords

• nonn
• easy
• base

Comments

In the definition, "position" refers to the position of the digit in the decimal expansion, starting counting at 1 for the least significant digit.

In the Example section, the notation a&b denotes the concatenation of two numbers, a and b.

a(n) = n for 2, 3, 5, 7, 11, 13, 17, 19, 101, 103, 107, 109, 113, ...

Examples

			p =   2 -> (2^1)             -> 2 (prime).
p =  23 -> (2^2)&(3^1)       -> 43 (prime).
p = 337 -> (3^3)&(3^2)&(7^1) -> 2797 (prime).
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..1000

Programs

Mathematica

f[n_] := Block[{d = Reverse@ IntegerDigits@ n, k}, FromDigits[Reap@ For[k = 1, k <= Length@ d, k++, Sow[d[[k]]^k]] // Flatten // Rest // Reverse // IntegerDigits // Flatten]]; Select[Prime@ Range@ 125, PrimeQ[f@ #] &] (* Michael De Vlieger, Apr 02 2015 *)

Python

import sympy
def powdig(m):
    l=len(str(m))
    return(int(''.join([str(int(list(i)[1])**(l-list(i)[0])) for i in enumerate(list(str(m)))])))
n=2
while n>0:
    t=powdig(n)
    if sympy.isprime(t)==True:
        print(n)
    n=sympy.nextprime(n)