A030482 Primes with property that when cubed all even digits occur together and all odd digits occur together.

2, 3, 11, 13, 17, 19, 31, 59, 71, 131, 137, 173, 179, 211, 293, 359, 431, 439, 587, 659, 1277, 4057, 6379, 13093, 13537, 15877, 25799, 28753, 29173, 36493, 39293, 39719, 40013, 60919, 66071, 69491, 73681, 87491, 126011, 137507, 138599, 189491, 199831, 201673

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Examples

			17 is a term as 17^3 = 4913 which has even digits on one end and odd digits at the other. - _David A. Corneth_, Mar 27 2021
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..107 (first 71 terms from Harvey P. Dale, terms <= 10^9)

Programs

Maple

q:= n-> (l-> add(irem(l[i]+l[i-1], 2), i=2..nops(l))<2)(convert(n^3, base, 10)):
select(q, [ithprime(n)$n=1..20000])[];  # Alois P. Heinz, Mar 27 2021

Mathematica

Select[Prime[Range[13000]],Length[Split[If[OddQ[#],1,0]&/@ IntegerDigits[ #^3]]]<3&] (* Harvey P. Dale, Dec 31 2013 *)

Python

from sympy import primerange
from itertools import groupby
def ok(n): return len([k for k, g in groupby([int(d in "13579") for d in str(n)])]) <= 2
def aupto(limit): return [p for p in primerange(2, limit+1) if ok(p**3)]
print(aupto(201673)) # Michael S. Branicky, Mar 27 2021

Extensions

Offset changed to 1 by David A. Corneth, Mar 27 2021