A080794 -id:A080794 - cp's OEIS frontend

A103174 Numbers k with increasing digits such that the digits of k appear among the digits of the k-th prime number.

7, 5789, 234567, 345679

Offset: 1

Labos Elemer, Feb 28 2005

We assume digits of k are in increasing order. No terms < 10^7.

Sequence is complete. - Giovanni Resta, Apr 29 2017

			n: {7, 5789, 234567, 345679}
prime(n): {17, 57089, 3264857, 4956733}

Cf. A080794, A068575, A075902.

Select[Rest@ Union[FromDigits /@ Subsets@ Range@ 9], SubsetQ @@ IntegerDigits@ {Prime@#, #} &] (* Giovanni Resta, Apr 29 2017 *)

Definition edited by Giovanni Resta, May 01 2017

A113898 Numbers k such that the value pi(k), the number of primes <= k, can be obtained deleting some of the repeating adjacent digits of k.

Original entry on oeis.org

1196, 11373, 22517, 33597, 44639, 55646, 60062, 61159, 62256, 63346, 63347, 64448, 64544, 64555, 64577, 64588, 64599, 64611, 64655, 64668, 64700, 64711, 64722, 64774, 64884, 64992, 65545, 65770, 65880, 65881, 65990, 66644, 67746, 68841

Offset: 1

Giovanni Resta, Jan 29 2006

Largest value below 10^7 is given by pi(110486) = 10486.

			pi(64668) = 6468, pi(99551) = 9551.

Cf. A000720, A114924, A080794.

lst = {}; p=0; While[p < 10^7, n=PrimePi[ ++p]; {sp, sn}=Split/@IntegerDigits@{p, n}; If[First/@sp==First/@sn && And@@GreaterEqual@@@Transpose[Length/@#&/@{sp, sn}], AppendTo[lst, p]]]; lst

A356980 Numbers k such that prime(k) can be written using only the digits of k (but they may used multiple times).

Original entry on oeis.org

137, 187, 321, 917, 1098, 1346, 1347, 1349, 1362, 1367, 1384, 1395, 1528, 1583, 1850, 1859, 1876, 1973, 2415, 2490, 2517, 2631, 2632, 2970, 3417, 3529, 3573, 3575, 3590, 3598, 3751, 3785, 3860, 4301, 4537, 4591, 4639, 4927, 4980, 4983, 5231, 5319, 5342, 5790, 6106, 6107

Offset: 1

Tanya Khovanova, Sep 09 2022

The digits of k can be reused. In other words, the distinct digits of prime(k) form a subset of the set of the distinct digits of k.

This sequence is infinite as every pandigital number is in this sequence, see A171102.

			The 137th prime number is 773, which can be written with the digits of 137. Thus 137 is in this sequence.

Cf. A171102, A080794.

Select[Range[10000], SubsetQ[Sort[IntegerDigits[#]], Sort[IntegerDigits[Prime[#]]]] &]

from sympy import nextprime
from itertools import count, islice
def agen(): # generator of terms
    pk = 2
    for k in count(1):
        if set(str(pk)) <= set(str(k)): yield k
        pk = nextprime(pk)
print(list(islice(agen(), 46))) # Michael S. Branicky, Sep 09 2022

cp's OEIS Frontend

A103174 Numbers k with increasing digits such that the digits of k appear among the digits of the k-th prime number.

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A113898 Numbers k such that the value pi(k), the number of primes <= k, can be obtained deleting some of the repeating adjacent digits of k.

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Mathematica

A356980 Numbers k such that prime(k) can be written using only the digits of k (but they may used multiple times).

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Mathematica

Python