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 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)). 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 22 22:38 EDT 2021. Contains 347609 sequences. (Running on oeis4.)