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%I A217565 #41 Aug 23 2021 08:36:44
%S A217565 33581,673,571,1987,915199,441799,2115761,961943,15406687,77123341,
%T A217565 4098427,5526679,54560189,22291639,371594479,126499693,229299227,
%U A217565 103196347,37851677,1198387109,801422893,966240103,281430131,926679973,154019941,196449137,243985993
%N 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)).
%C A217565 This reverses the idea for A217049, with the smaller of successive primes being raised to the larger prime power. See that sequence for motivation.
%e A217565 (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.
%t A217565 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 *)
%o A217565 (Python)
%o A217565 from sympy import isprime, nextprime, prime
%o A217565 from sympy.ntheory import count_digits
%o A217565 def a(n):
%o A217565     pn = prime(n); qn = nextprime(pn)
%o A217565     p, q = 2, 3; c = count_digits((q**pn)*(p**qn))
%o A217565     while not all(isprime(c[i]) for i in range(10)):
%o A217565         p, q = q, nextprime(q); c = count_digits((q**pn)*(p**qn))
%o A217565     return p
%o A217565 print([a(n) for n in range(1, 7)]) # _Michael S. Branicky_, Aug 21 2021
%Y A217565 Cf. A217049.
%K A217565 nonn,base
%O A217565 1,1
%A A217565 _James G. Merickel_, Oct 06 2012
%E A217565 a(15) added by _James G. Merickel_, Oct 17 2012
%E A217565 Name clarified by _Tanya Khovanova_, Aug 17 2021
%E A217565 a(16)-a(20) added by _Giorgos Kalogeropoulos_, Aug 18 2021
%E A217565 a(21)-a(27) from _Michael S. Branicky_, Aug 22 2021

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