A186280 Primes within A186279.

41, 47, 89, 131, 167, 233, 257, 269, 293, 311, 317, 359, 401, 431, 449, 521, 593, 617, 647, 653, 701, 773, 797, 809, 941, 953, 971, 977, 983, 1097, 1151, 1187, 1229, 1259, 1283, 1319, 1409, 1427, 1481, 1493, 1571, 1583, 1607, 1619, 1667, 1871, 1877, 1889, 1907, 1913, 1931, 1949, 1979

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

filter:= n -> isprime(n) and isprime(convert(convert(n, base, 10), `+`)+convert(convert(n^2, base, 10), `+`)+convert(convert(n^3, base, 10), `+`)):
select(filter, [seq(i, i=5..10000, 6)]); # Robert Israel, Jul 28 2020

Mathematica

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

Crossrefs

Cf. A186278, A186279.

Sequence in context: A180547 A329446 A243460 * A039328 A043151 A043931

Adjacent sequences: A186277 A186278 A186279 * A186281 A186282 A186283

Keyword

nonn,easy,base

Author

Harvey P. Dale, Feb 16 2011

Status

approved