A355539 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.

1, 6, 19, 97, 103, 110, 2065, 2515, 3261, 25562

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Example

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.
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.

Mathematica

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 *)

Prog

(Python)
from itertools import count, islice
from sympy import nextprime
def A355539_gen(): # generator of terms
    p, s, k = 2, set(), 0
    for i in count(1):
        if int(a:=''.join(sorted(str(p))))==int(b:=''.join(sorted(str(i)))):
            k += 1
            if (q:=(a.count('0'), b.count('0'))) not in s:
                yield k
                s.add(q)
        p = nextprime(p)
A355539_list = list(islice(A355539_gen(), 5)) # Chai Wah Wu, Jul 07 2022

Crossrefs

Cf. A355318, A355317.

Sequence in context: A111510 A151277 A192368 * A323686 A285853 A138748

Adjacent sequences: A355536 A355537 A355538 * A355540 A355541 A355542

Keyword

nonn,base,more

Author

Xiaofeng Wang, Jul 06 2022

Status

approved