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%I #12 Aug 24 2022 10:00:31
%S 1,6,19,97,103,110,2065,2515,3261,25562
%N a(1) = 1; for n >= 2, a(n) is the earliest occurrence k of the next distinct pair {x(k), y(k)}, where x(k) and y(k) denote the count of zero digits in A355318(k) and A355317(k), respectively.
%e 6 is a term since {x(6), y(6)} is the earliest occurrence of {1, 2}, which means A355318(6) = 6106 has 1 zero digit, and A355317(6) = 60601 has 2 zero digits.
%e 25562 is a term since {x(25562), y(25562)} is the earliest occurrence of {5, 6}, which means A355318(25562) = 1300020350 has 5 zero digits, and A355317(25562) = 30000350201 has 6 zero digits.
%t a[max_] := Block[{p, b, x, y}, p = Module[{l}, Select[{#, Prime[#]} & /@ Range[max], (l = IntegerDigits[#[[2]]]; SortBy[Tally[l], First] === SortBy[Tally[PadLeft[IntegerDigits[#[[1]]], Length[l]]], First]) &]]; Do[{x, y} = {Count[IntegerDigits[p[[i, 1]]], 0], Count[IntegerDigits[p[[i, 2]]], 0]}; If[! IntegerQ[b[x, y]], b[x, y] = i], {i, Length[p]}]; Sort[DownValues[b][[All, 2]]]]; a[100010000] (* Gives the first 9 terms *)
%o (Python)
%o from itertools import count, islice
%o from sympy import nextprime
%o def A355539_gen(): # generator of terms
%o p, s, k = 2, set(), 0
%o for i in count(1):
%o if int(a:=''.join(sorted(str(p))))==int(b:=''.join(sorted(str(i)))):
%o k += 1
%o if (q:=(a.count('0'),b.count('0'))) not in s:
%o yield k
%o s.add(q)
%o p = nextprime(p)
%o A355539_list = list(islice(A355539_gen(),5)) # _Chai Wah Wu_, Jul 07 2022
%Y Cf. A355318, A355317.
%K nonn,base,more
%O 1,2
%A _Xiaofeng Wang_, Jul 06 2022
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