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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A020610 A351682 A257529 * A019366 A045334 A244392

Adjacent sequences: A030479 A030480 A030481 * A030483 A030484 A030485

Keyword

nonn,base

Author

Patrick De Geest

Extensions

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

Status

approved