A030086 -id:A030086 - 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

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

Original entry on oeis.org

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

Patrick De Geest, Dec 11 1999

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

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

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

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

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

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

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

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

A030088 a(n) = prime^2 and digits of prime do not appear in a(n).

Original entry on oeis.org

4, 9, 49, 289, 841, 2209, 2809, 3481, 4489, 6241, 24649, 29929, 66049, 94249, 97969, 121801, 124609, 128881, 167281, 201601, 218089, 299209, 310249, 332929, 434281, 452929, 458329, 546121, 619369, 727609, 863041, 2093809

Offset: 1

Patrick De Geest

Harvey P. Dale, Table of n, a(n) for n = 1..442 (All terms up to the 10 millionth prime.)

Cf. A030086.

Subsequence of A001248.

R:= NULL: count:= 0: p:= 0:
while count < 40 do
  p:= nextprime(p);
  ps:= p^2;
  if convert(convert(p,base,10),set) intersect convert(convert(ps,base,10),set) = {} then
    R:= R, ps; count:= count+1
  fi
od:
R; # Robert Israel, Nov 02 2022

Select[Prime[Range[250]],Intersection[IntegerDigits[#],IntegerDigits[#^2]]=={}&]^2 (* Harvey P. Dale, May 18 2024 *)

a(n) = A030086(n)^2. - Robert Israel, Nov 02 2022

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

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

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A030088 a(n) = prime^2 and digits of prime do not appear in a(n).

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