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Numbers k such that k has nonincreasing digits and the k-th prime has nondecreasing digits.
4

%I #9 Jun 27 2022 15:58:08

%S 1,2,3,4,5,6,7,8,9,10,22,30,31,33,41,50,51,52,55,70,72,73,75,77,87,88,

%T 91,92,95,200,222,332,333,430,633,644,654,733,861,862,872,887,986,

%U 6666,7655,7662,86540,86543,86550,86552,86553,86621,86622,86630,86631

%N Numbers k such that k has nonincreasing digits and the k-th prime has nondecreasing digits.

%H Michael S. Branicky, <a href="/A116069/b116069.txt">Table of n, a(n) for n = 1..75</a> (all terms < 10^9)

%e p(86543) = 1111189.

%o (Python)

%o from sympy import sieve

%o from itertools import count, islice, combinations_with_replacement as mc

%o def nd(n): s = str(n); return s == "".join(sorted(s))

%o def bgen(d):

%o ni = map(int, ("".join(m) for m in mc("9876543210", d)))

%o yield from sorted(k for k in ni if k != 0)

%o def agen():

%o for d in count(1):

%o yield from (k for k in bgen(d) if nd(sieve[k]))

%o print(list(islice(agen(), 55))) # _Michael S. Branicky_, Jun 26 2022

%Y Cf. A116066, A116067, A116068.

%K nonn,base

%O 1,2

%A _Giovanni Resta_, Feb 13 2006