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Primes p such that digits of p do not appear in p^4.
6

%I #35 Jan 05 2022 10:43:25

%S 2,3,7,53,59,67,89,383,887,2027,3253,5669,7993,8009,9059,53633,54667,

%T 56533,88883,272777777,299222299,383833883,797769997

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

%C Primes in A111116.

%C No further terms up to 10^9. - _Felix Fröhlich_, Jan 04 2015

%C No further terms up to 10^10. - _Chai Wah Wu_, Jan 06 2015

%C No further terms up to 2.5*10^13 - _Giovanni Resta_, Jun 01 2015

%C No further terms up to 10^19 (via A111116). - _Michael S. Branicky_, Jan 05 2022

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

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

%o (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

%o (Python)

%o from sympy import isprime

%o A253574_list = [n for n in range(1,10**6) if set(str(n)) & set(str(n**4)) == set() and isprime(n)]

%o # _Chai Wah Wu_, Jan 06 2015

%Y Cf. A111116.

%Y 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).

%K nonn,base,more

%O 1,1

%A _Vincenzo Librandi_, Jan 04 2015

%E a(20)-a(23) from _Felix Fröhlich_, Jan 04 2015