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

%I A255073 #26 May 22 2025 10:21:42
%S A255073 2,3,5,7,11,13,17,19,23,37,43,47,67,71,79,83,101,103,107,109,113,131,
%T A255073 137,139,167,173,179,191,211,241,263,269,281,307,311,313,331,337,353,
%U A255073 359,367,397,431,479,491,503,521,577,593,601,613,617,659,673
%N A255073 Primes that remain prime after each digit is replaced by the power of its position.
%C A255073 In the definition, "position" refers to the position of the digit in the decimal expansion, starting counting at 1 for the least significant digit.
%C A255073 In the Example section, the notation a&b denotes the concatenation of two numbers, a and b.
%C A255073 a(n) = n for 2, 3, 5, 7, 11, 13, 17, 19, 101, 103, 107, 109, 113, ...
%H A255073 Abhiram R Devesh, <a href="/A255073/b255073.txt">Table of n, a(n) for n = 1..1000</a>
%e A255073 p =   2 -> (2^1)             -> 2 (prime).
%e A255073 p =  23 -> (2^2)&(3^1)       -> 43 (prime).
%e A255073 p = 337 -> (3^3)&(3^2)&(7^1) -> 2797 (prime).
%t A255073 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 *)
%o A255073 (Python)
%o A255073 import sympy
%o A255073 def powdig(m):
%o A255073     l=len(str(m))
%o A255073     return(int(''.join([str(int(list(i)[1])**(l-list(i)[0])) for i in enumerate(list(str(m)))])))
%o A255073 n=2
%o A255073 while n>0:
%o A255073     t=powdig(n)
%o A255073     if sympy.isprime(t)==True:
%o A255073         print(n)
%o A255073     n=sympy.nextprime(n)
%K A255073 nonn,easy,base
%O A255073 1,1
%A A255073 _Abhiram R Devesh_, Feb 14 2015