A253576 -id:A253576 - cp's OEIS frontend

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

Vincenzo Librandi, Jan 04 2015

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

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

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).

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

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

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

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

A281678 Numbers k that have no digits in common with k^7.

Original entry on oeis.org

3, 7, 8, 33, 43, 77, 93, 272, 332, 662, 7757, 31333

Offset: 1

Robert Israel, Jan 26 2017

All terms have last digit 2, 3, 7 or 8.
Sequence is likely to be finite. If it exists, a(13) > 10^7.
In this sequence, the only terms with no repeated digits are 3, 7, 8, 43, 93. - Altug Alkan, Jan 26 2017
If it exists, a(13) > 10^17. - David Radcliffe, May 26 2025

			43 is a term because 43^7 = 271818611107 has no digit 4 or 3.

Cf. A001015. Contains A253576.

Cf. A281148.

select(t -> convert(convert(t,base,10),set) intersect convert(convert(t^7,base,10),set) = {},
{seq(seq(10*i+j,j=[2,3,7,8]),i=0..10^4});

Select[Range[40000], Intersection[IntegerDigits[#], IntegerDigits[ #^7]] == {}&] (* Vincenzo Librandi, Jan 27 2017 *)

isok(n) = #setintersect(Set(digits(n)), Set(digits(n^7))) == 0; \\ Michel Marcus, Jan 26 2017

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Python

Extensions