A253574 Primes p such that digits of p do not appear in p^4.

2, 3, 7, 53, 59, 67, 89, 383, 887, 2027, 3253, 5669, 7993, 8009, 9059, 53633, 54667, 56533, 88883, 272777777, 299222299, 383833883, 797769997

Offset: 1

Author

Vincenzo Librandi, Jan 04 2015

Keywords

• nonn
• base
• more

Comments

Primes in A111116.

No further terms up to 10^9. - Felix Fröhlich, Jan 04 2015

No further terms up to 10^10. - Chai Wah Wu, Jan 06 2015

No further terms up to 2.5*10^13 - Giovanni Resta, Jun 01 2015

No further terms up to 10^19 (via A111116). - Michael S. Branicky, Jan 05 2022

Examples

			2 and 2^4=16 have no digits in common, hence 2 is in the sequence.
		

Crossrefs

Cf. A111116.

Cf. primes such that digits of p do not appear in p^k: A030086 (k=2), A030087 (k=3), this sequence (k=4), no terms (k=5), A253575 (k=6), A253576 (k=7), A253577 (k=8), no terms (k=9), A253578 (k=10).

Programs

Mathematica

Select[Prime[Range[1000000]], Intersection[IntegerDigits[#], IntegerDigits[#^4]]=={} &]

PARI

forprime(p=1, 1e9, dip=digits(p); dipf=digits(p^4); sharedi=0; for(i=1, #dip, for(j=1, #dipf, if(dip[i]==dipf[j], sharedi++; break({2})))); if(sharedi==0, print1(p, ", "))) \\ Felix Fröhlich, Jan 04 2015

Python

from sympy import isprime
A253574_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**4)) == set() and isprime(n)]
# Chai Wah Wu, Jan 06 2015

Extensions

a(20)-a(23) from Felix Fröhlich, Jan 04 2015