A355318 Indices of the primes that have the same base-10 digits as the corresponding prime number (with multiplicity), disregarding zero digits.

751, 2971, 5174, 5594, 5789, 6106, 6151, 6376, 6613, 7129, 12376, 23719, 24758, 47135, 53146, 73906, 73969, 74956, 96512, 111406, 114475, 119825, 126896, 128377, 131657, 135815, 135817, 137681, 152402, 158924, 182045, 192641, 197269, 203383, 203758, 215809, 218332, 230261, 230431, 232946, 233485, 235918

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Example

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

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, 1]] (* 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 k
        k, pk = k+1, nextprime(pk)
print(list(islice(agen(), 32))) # Michael S. Branicky, Jun 28 2022
(PARI) strip0(v) = {my(nn=1); while(v[nn]==0, nn++); v[nn..#v]};
a355318(upto) = {my(k=0); forprime (p=2, upto, k++; if(strip0(vecsort(digits(k))) == strip0(vecsort(digits(p))), print1(k, ", ")))};
a355318(4000000); \\ Hugo Pfoertner, Jul 05 2022

Crossrefs

Cf. A355317 (the corresponding primes), A355539.

Sequence in context: A291524 A373206 A020391 * A252807 A332000 A223447

Adjacent sequences: A355315 A355316 A355317 * A355319 A355320 A355321

Keyword

base,easy,nonn

Author

Xiaofeng Wang, Jun 28 2022

Status

approved