A232116 Primes such that the sum of each nonzero digit raised to itself is prime.

11, 23, 41, 43, 47, 101, 113, 131, 157, 263, 311, 401, 571, 751, 829, 997, 1013, 1031, 1103, 1187, 1301, 1433, 1583, 1619, 1871, 2003, 2063, 2089, 2111, 2221, 2357, 2579, 2683, 2753, 2957, 3011, 3257, 3343, 3413, 3433, 3527, 3581, 3637, 3673, 3851, 4001, 4003, 4007, 4133, 4441, 4481, 4597, 4649

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

43 is a member of this sequence because 43 is prime and 4^4 + 3^3 = 256 + 27 = 283 is also prime.
263 is a member of this sequence because 263 is prime and 2^2 + 6^6 + 3^3 = 4 + 46656 + 27 = 46687 is also prime.

Prog

(Python)
from sympy import isprime, primerange
def Pow(n):
    s = 0
    for i in str(n):
        k = int(i)
        if k:
            s += k**k
    return s
{print(pn, end=', ') for pn in primerange(1, 2000) if isprime(Pow(pn))}
## Simplified by Derek Orr, Apr 05 2015
(PARI) sdiz(n) = {digs = digits(n); sum(i=1, #digs, if (digs[i], digs[i]^digs[i], 0)); }
lista(nn) = {forprime(n=1, nn, if (isprime(sdiz(n)), print1(n, ", "))); } \\ Michel Marcus, Nov 21 2013
(PARI)
has(n)=ispseudoprime(vecsum([x^x|x<-digits(n), x]))
select(has, primes(1000)) \\ Charles R Greathouse IV, Nov 21 2013

Crossrefs

Cf. A000040, A045512.

Sequence in context: A130282 A019356 A046440 * A119890 A094376 A086524

Adjacent sequences: A232113 A232114 A232115 * A232117 A232118 A232119

Keyword

nonn,base

Author

Derek Orr, Nov 19 2013

Status

approved