A355317 Prime numbers that have the same base-10 digits as their prime index (with multiplicity), disregarding zero digits.

5701, 27091, 50417, 55049, 57089, 60601, 61051, 63607, 66301, 72019, 132607, 270913, 284057, 574031, 654301, 936007, 936907, 950647, 1250609, 1461001, 1504417, 1580921, 1682069, 1703287, 1750631, 1810553, 1810573, 1837601, 2050241, 2145089, 2485001, 2641109, 2709169, 2800333, 2805703

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Example

15097067 is a term since its index primepi(15097067) = 976571 shares the same multiset of nonzero digits {1,5,6,7,7,9}.

Mathematica

a[max_] := Module[{l}, Select[{#, Prime[#]} & /@ Range[max], (l = IntegerDigits[#[[2]]]; SortBy[Tally[l], First] === SortBy[Tally[PadLeft[IntegerDigits[#[[1]]], Length[l]]], First]) &]]; a[10^6][[All, 2]] (* Gives the first 108 terms *)

Prog

(Python)
from sympy import nextprime
from itertools import islice
def b10s(n): return "".join(sorted(str(n))).lstrip("0")
def agen():
    k, pk = 1, 2
    while True:
        if b10s(k) == b10s(pk): yield pk
        k, pk = k+1, nextprime(pk)
print(list(islice(agen(), 32))) # Michael S. Branicky, Jun 28 2022
(PARI) digs(k) = vecsort(select(x->(x>0), digits(k)));
isok(p) = if (isprime(p), digs(p) == digs(primepi(p))); \\ Michel Marcus, Jul 05 2022

Crossrefs

Cf. A355318 (the prime indices), A355539.

Cf. A355418.

Sequence in context: A269344 A184147 A235207 * A252342 A237743 A025027

Adjacent sequences: A355314 A355315 A355316 * A355318 A355319 A355320

Keyword

base,easy,nonn

Author

Xiaofeng Wang, Jun 28 2022

Status

approved