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A180404 Primes p such that the sum of fifth power of their digits is a prime. 1
11, 101, 191, 223, 227, 229, 281, 313, 331, 337, 359, 373, 379, 397, 463, 487, 557, 577, 593, 643, 683, 733, 739, 757, 773, 821, 863, 881, 911, 937, 953, 1019, 1033, 1091, 1109, 1123, 1129, 1181, 1213, 1231, 1259, 1277, 1291, 1303, 1321, 1381, 1433, 1439 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..48.

FORMULA

If a prime p = abcdef... (each letter being a single digit) then sum = a^5+b^5+... belongs to this sequence if sum is a prime.

EXAMPLE

a(5) = 227 since 2^5+2^5+7^5 = 32+32+16807 = 16871 is a prime.

MAPLE

P:=proc(n) local a, k; a:=convert(ithprime(n), base, 10);

if isprime(add(a[k]^5, k=1..nops(a))) then ithprime(n); fi;  end:

seq(P(i), i=1..228); # Paolo P. Lava, Sep 24 2018

MATHEMATICA

Select[Prime[Range[500]], PrimeQ[Total[IntegerDigits[#]^5]]&] (* Harvey P. Dale, May 25 2011 *)

CROSSREFS

Cf. A046704, A052034, A091366, A091367.

Sequence in context: A199328 A068188 A032592 * A142317 A180406 A174884

Adjacent sequences:  A180401 A180402 A180403 * A180405 A180406 A180407

KEYWORD

nonn,base

AUTHOR

Carmine Suriano, Sep 02 2010

STATUS

approved

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Last modified July 25 02:57 EDT 2021. Contains 346282 sequences. (Running on oeis4.)