A217565 The smallest prime p that with its successor q gives prime counts of all ten base-10 digits for the expression (q^prime(n))*(p^prime(n+1)).

33581, 673, 571, 1987, 915199, 441799, 2115761, 961943, 15406687, 77123341, 4098427, 5526679, 54560189, 22291639, 371594479, 126499693, 229299227, 103196347, 37851677, 1198387109, 801422893, 966240103, 281430131, 926679973, 154019941, 196449137, 243985993

Offset

1,1

Comments

This reverses the idea for A217049, with the smaller of successive primes being raised to the larger prime power. See that sequence for motivation.

Links

Table of n, a(n) for n=1..27.

Example

(677^3)*(673^5) is the value corresponding to a(2).  What this means is that the decimal representation of this number has a prime number of copies of each digit and no pair of successive primes in the same order and smaller than {673,677} has the same characteristic.

Mathematica

Table[p=2; While[!And@@PrimeQ[DigitCount[(p^Prime[n+1])*(NextPrime@p^Prime[n])]], p=NextPrime@p]; p, {n, 6}] (* Giorgos Kalogeropoulos, Aug 18 2021 *)

Prog

(Python)
from sympy import isprime, nextprime, prime
from sympy.ntheory import count_digits
def a(n):
    pn = prime(n); qn = nextprime(pn)
    p, q = 2, 3; c = count_digits((q**pn)*(p**qn))
    while not all(isprime(c[i]) for i in range(10)):
        p, q = q, nextprime(q); c = count_digits((q**pn)*(p**qn))
    return p
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Aug 21 2021

Crossrefs

Cf. A217049.

Sequence in context: A235678 A235448 A236197 * A142587 A116496 A235667

Adjacent sequences: A217562 A217563 A217564 * A217566 A217567 A217568

Keyword

nonn,base

Author

James G. Merickel, Oct 06 2012

Extensions

a(15) added by James G. Merickel, Oct 17 2012

Name clarified by Tanya Khovanova, Aug 17 2021

a(16)-a(20) added by Giorgos Kalogeropoulos, Aug 18 2021

a(21)-a(27) from Michael S. Branicky, Aug 22 2021

Status

approved