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Primes within A186279.
2

%I #14 Jul 28 2020 11:07:53

%S 41,47,89,131,167,233,257,269,293,311,317,359,401,431,449,521,593,617,

%T 647,653,701,773,797,809,941,953,971,977,983,1097,1151,1187,1229,1259,

%U 1283,1319,1409,1427,1481,1493,1571,1583,1607,1619,1667,1871,1877,1889,1907,1913,1931,1949,1979

%N Primes within A186279.

%H Robert Israel, <a href="/A186280/b186280.txt">Table of n, a(n) for n = 1..10000</a>

%e 257 is in the sequence because (1) it is prime and (2) the sum of its digits (2 + 5 + 7 = 14) plus the sum of the digits of 257^2 (66049 -> 6 + 6 + 0 + 4 + 9 = 25) plus the sum of the digits of 257^3 (16974593 -> 1 + 6 + 9 + 7 + 4 + 5 + 9 + 3 = 44) equals 14 + 25 + 44 = 83, which is prime.

%p filter:= n -> isprime(n) and isprime(convert(convert(n,base,10),`+`)+convert(convert(n^2,base,10),`+`)+convert(convert(n^3,base,10),`+`)):

%p select(filter, [seq(i,i=5..10000,6)]); # _Robert Israel_, Jul 28 2020

%t Select[Prime[Range[300]], PrimeQ[Total[IntegerDigits[#]] + Total[IntegerDigits[#^2]] + Total[IntegerDigits[#^3]]]&]

%Y Cf. A186278, A186279.

%K nonn,easy,base

%O 1,1

%A _Harvey P. Dale_, Feb 16 2011