A365678 Primes p whose index has a submultiset of their decimal digits.

17, 367, 491, 1327, 1823, 2039, 2131, 2143, 2153, 2693, 4621, 5417, 5701, 6481, 6883, 7459, 7691, 10723, 11483, 11593, 12491, 12497, 12853, 14723, 15287, 17093, 24781, 25849, 26951, 27091, 27179, 33569, 33967, 34367, 35171, 35809, 39451, 40283, 41263, 41543, 41983, 42437, 45971

Offset

1,1

Comments

Number of terms < 10^k, k > 0: 0, 1, 3, 17, 132, 379, 1422, 7156, 39004, 237792, ...

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

a(1) is 17 since 17 is the 7th prime;
a(2) is not 31 since it is the 11th prime;
a(2) is 367 since it is the 73rd prime;
a(3) is 491 since it is the 94th prime;
a(237793) = 10000865549 since it is the 455090018th prime; etc.

Mathematica

idx = 1; p = 2; lst = {}; While[p < 50001, If[ MemberQ[ Subsets[ Sort@ IntegerDigits@ p, IntegerLength@ idx], Sort@ IntegerDigits@ idx], AppendTo[lst, p]; Print[{p, idx}]]; idx++; p = NextPrime@p]; lst

Prog

(Python)
from sympy import nextprime
from itertools import islice
from collections import Counter
def agen(): # generator of terms
    i, p = 1, 2
    while True:
        if Counter(str(i)) <= Counter(str(p)): yield p
        i, p = i+1, nextprime(p)
print(list(islice(agen(), 43))) # Michael S. Branicky, Sep 15 2023

Crossrefs

Cf. A000040, A355418.

Sequence in context: A120287 A222678 A293691 * A002197 A070148 A097499

Adjacent sequences: A365675 A365676 A365677 * A365679 A365680 A365681

Keyword

base,nonn

Author

Robert G. Wilson v, Sep 15 2023

Status

approved