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

1,1

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, ...

Links

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

Example

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

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 *)

Prog

(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)

Crossrefs

Sequence in context: A262363 A050264 A075239 * A341667 A330007 A008792

Adjacent sequences: A255070 A255071 A255072 * A255074 A255075 A255076

Keyword

nonn,easy,base

Author

Abhiram R Devesh, Feb 14 2015

Status

approved