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

%I A030482 #24 Mar 27 2021 23:13:27
%S A030482 2,3,11,13,17,19,31,59,71,131,137,173,179,211,293,359,431,439,587,659,
%T A030482 1277,4057,6379,13093,13537,15877,25799,28753,29173,36493,39293,39719,
%U A030482 40013,60919,66071,69491,73681,87491,126011,137507,138599,189491,199831,201673
%N A030482 Primes with property that when cubed all even digits occur together and all odd digits occur together.
%H A030482 David A. Corneth, <a href="/A030482/b030482.txt">Table of n, a(n) for n = 1..107</a> (first 71 terms from Harvey P. Dale, terms <= 10^9)
%e A030482 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
%p A030482 q:= n-> (l-> add(irem(l[i]+l[i-1], 2), i=2..nops(l))<2)(convert(n^3, base, 10)):
%p A030482 select(q, [ithprime(n)$n=1..20000])[];  # _Alois P. Heinz_, Mar 27 2021
%t A030482 Select[Prime[Range[13000]],Length[Split[If[OddQ[#],1,0]&/@ IntegerDigits[ #^3]]]<3&] (* _Harvey P. Dale_, Dec 31 2013 *)
%o A030482 (Python)
%o A030482 from sympy import primerange
%o A030482 from itertools import groupby
%o A030482 def ok(n): return len([k for k, g in groupby([int(d in "13579") for d in str(n)])]) <= 2
%o A030482 def aupto(limit): return [p for p in primerange(2, limit+1) if ok(p**3)]
%o A030482 print(aupto(201673)) # _Michael S. Branicky_, Mar 27 2021
%K A030482 nonn,base
%O A030482 1,1
%A A030482 _Patrick De Geest_
%E A030482 Offset changed to 1 by _David A. Corneth_, Mar 27 2021