A253577 -id:A253577 - 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

A253606 Numbers n such that digits of n are not present in n^8.

Original entry on oeis.org

3, 4, 8, 9, 22, 33, 43, 54, 59, 73, 222, 233, 353, 712, 777, 22224

Offset: 1

Chai Wah Wu, Jan 05 2015

a(17) > 10^9.

			4^8 = 65536 which does not contain the digit 4.

Cf. A111116, A253577.

a253606[n_] := Block[{f},
  f[x_] := MemberQ[IntegerDigits[x^8], #] & /@ IntegerDigits[x];
Select[Range@n, DeleteDuplicates@f[#] == {False} &]]; a253606[10^5] (* Michael De Vlieger, Jan 06 2015 *)

A253606_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**8)) == set()]

cp's OEIS Frontend

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

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