A030087 Primes such that digits of p do not appear in p^3.

2, 3, 7, 43, 47, 53, 157, 223, 263, 487, 577, 587, 823, 4657, 5657, 6653, 7177, 8287, 9343, 26777, 36293, 46477, 58787, 72727, 75707, 176777, 363313, 530353, 566653, 959953, 1771787, 2525557, 2555353, 2626277, 3656363, 4414447, 7110707, 8448343, 20700077, 54475457, 71117177, 72722977, 135135113, 393321293, 457887457, 505053053, 672722627

Offset: 1

Author

Patrick De Geest, Dec 11 1999

Keywords

• nonn
• base

Comments

Primes of sequence A029785. - Michel Marcus, Jan 04 2015

Examples

			2 and 2^3=8 have no digits in common, hence 2 is in the sequence.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..86 (terms < 10^19; terms 74..86 via A029785)

Crossrefs

Cf. A029785 (digits of n are not present in n^3), A030086 (similar, with p^2), A253574 (similar, with p^4).

Programs

Mathematica

Select[Prime[Range[1500000]], Intersection[IntegerDigits[#], IntegerDigits[#^3]]=={} &] (* Vincenzo Librandi, Jan 04 2015 *)

PARI

lista(nn) = {forprime (n=1, nn, if (#setintersect(Set(vecsort(digits(n^3))), Set(vecsort(digits(n)))) == 0, print1(n, ", ")); ); } \\ Michel Marcus, Jan 04 2015

Python

from sympy import isprime
A030087_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**3)) == set() and isprime(n)]
# Chai Wah Wu, Jan 05 2015

Extensions

Changed offset from 0 to 1 and more terms from Vincenzo Librandi, Jan 04 2015

a(40)-a(47) from Chai Wah Wu, Jan 05 2015