A217049 Least prime p such that all ten base-10 digits have prime counts in (p^prime(n))*(q^prime(n+1)), where q is the next prime after p.

18329, 1913, 1063, 109, 932839, 85061, 29729989, 5653759, 1958731, 20891539, 35008723, 28265837, 2, 3, 6238777, 276624683, 92343187, 24205651, 49598321, 17722981, 46741657, 219329923, 297614029, 106791577, 621528749, 217893821, 113824657, 122670287, 81263857

Offset

1,1

Comments

Motivation for this sequence stems from the coincidence that (2^41)*(3^43) and (3^43)*(5^47) give prime counts for their digits.

Links

Table of n, a(n) for n=1..29.

Example

(18329^2)*(18341^3) = 2072748335390985614861 has digit counts [2,2,2,3,2,2,2,2,3,2], all primes, and replacing the pair (18329,18341) with a smaller pair fails this criterion. In particular, (3733^2)*(3739^3) = 728420861672094091 has digit counts [3,2,3,0,2,0,2,2,2,2], not all prime.

Mathematica

Table[p=2; While[!And@@PrimeQ[DigitCount[(p^Prime@n)*(NextPrime@p^Prime[n+1])]], 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(p**pn*q**qn)
    while not all(isprime(c[i]) for i in range(10)):
        p, q = q, nextprime(q); c = count_digits(p**pn*q**qn)
    return p
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Aug 20 2021

Crossrefs

Cf. A216854.

Sequence in context: A237737 A145822 A286035 * A251025 A203783 A071368

Adjacent sequences: A217046 A217047 A217048 * A217050 A217051 A217052

Keyword

nonn,base

Author

James G. Merickel, Sep 25 2012

Extensions

Name clarified by Tanya Khovanova, Aug 17 2021

a(23)-a(29) from Michael S. Branicky, Aug 25 2021

Name edited by Michel Marcus and Michael S. Branicky, Aug 25 2021

Status

approved