A039999 -id:A039999 - cp's OEIS frontend

A052494 Number of different primes that can be formed by permuting digits of n-th prime.

1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 3, 3, 2, 4, 1, 3, 3, 3, 3, 4, 2, 2, 2, 4, 3, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 3, 2, 3, 2, 3, 2, 2, 1, 3, 2, 3, 4, 1, 3, 4, 1, 1, 4, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 4, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 3

Offset: 2

Enoch Haga, Mar 16 2000

Leading zeros not permitted, so, e.g., prime(27) = 103 but a(27) = 1 even though 13 and 31 are both primes. - Harvey P. Dale, Dec 17 2012

			a(75)=4 because the digits in 379 may be arranged to form a total of 4 primes: 379, 397, 739 and 937.

A039999, A046810.

ndp[n_]:=Module[{pers=FromDigits/@Permutations[IntegerDigits[n]]}, Count[ pers,?(IntegerLength[#]==IntegerLength[n]&&PrimeQ[#]&)]]; ndp/@ Prime[ Range[110]] (* _Harvey P. Dale, Dec 17 2012 *)

A118553 Number of permutations of digits of n which denote perfect power.

Original entry on oeis.org

1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0

Offset: 1

Giovanni Teofilatto, May 07 2006

Cf. A039999.

A328515 Number of primes in permutations of digits per permutation class of the positive integers ordered by smallest member of this class excluding leading zeros.

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0, 1, 0, 1, 3, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 0, 3, 3, 0, 2, 0, 1, 2, 0, 0, 4, 0, 0, 3, 0, 0

Offset: 0

David A. Corneth, Oct 18 2019

Primitive sequence of A039999.

			A179239(67) = 103. Its permutations of digits without leading zeros are 103, 130, 301, 310. Of these, only 103 is prime which is one number. So a(67) = 1.

David A. Corneth, Table of n, a(n) for n = 0..9999

Cf. A039999, A166921, A179239.

A039998 Primes embedded in prime(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 3, 4, 2, 3, 2, 3, 3, 2, 4, 1, 3, 3, 3, 3, 4, 2, 2, 2, 4, 3, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 1, 3, 2, 3, 4, 1, 3, 4, 2, 1, 4, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 3

Offset: 1

David W. Wilson

a(n) counts permutations of digits of prime(n) which denote primes.

a(n) = A039999(prime(n)).

A086151 Number of permutations of decimal digits of 2^n which yield a prime.

Original entry on oeis.org

1, 0, 0, 1, 1, 0, 2, 0, 2, 4, 0, 0, 5, 19, 10, 3, 87, 9, 0, 377, 293, 84, 9, 265, 142, 502, 4916, 979, 30453, 38758, 15274, 5270, 10463, 81628, 69189, 91023, 1605954, 378559, 152874, 3447170, 220776, 4350954, 1746163, 51889555, 12949705, 5145813, 202624585, 404342074, 118292490

Offset: 1

Labos Elemer, Aug 04 2003

			n=19: 2^19 = 524288, has 180 permutations, each composite, a(19)=0;
n=13: 2^13 = 8192, the following 5 of the 24 permutations provide primes: {8219, 8291, 1289, 9281, 2819}.

Cf. A039999, A086150, A000079.

Table[Count[Table[PrimeQ[tn[Part[Permutations[ IntegerDigits[2^w]], j]]], {j, 1, Length[Permutations[ IntegerDigits[2^w]]]}], True], {w, 1, 20}]

\\ here b(n) is A039999.
b(n)={my(D=vecsort(digits(n)), S=0); forperm(D, p, if(isprime(fromdigits(Vec(p))),  S++)); S}
{ for(n=1, 30, print1(b(2^n), ", ")) } \\ Andrew Howroyd, Jan 05 2020

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations as mp
def a(n): return sum(1 for p in mp(str(2**n)) if isprime(int("".join(p))))
print([a(n) for n in range(1, 31)]) # Michael S. Branicky, May 25 2023

a(n) = A039999(A000079(n)).

a(27)-a(44) from Andrew Howroyd, Jan 05 2020

a(45)-a(49) from Michael S. Branicky, May 26 2023

A118626 Number of permutations of digits of n which denote a palindromic number.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0

Offset: 1

Giovanni Teofilatto, May 09 2006

Cf. A039999, A118553.

cp's OEIS Frontend

A052494 Number of different primes that can be formed by permuting digits of n-th prime.

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A118553 Number of permutations of digits of n which denote perfect power.

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A328515 Number of primes in permutations of digits per permutation class of the positive integers ordered by smallest member of this class excluding leading zeros.

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A039998 Primes embedded in prime(n).

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A086151 Number of permutations of decimal digits of 2^n which yield a prime.

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A118626 Number of permutations of digits of n which denote a palindromic number.

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