A114924 -id:A114924 - cp's OEIS frontend

A362066 Primes associated with the indices in A362060.

17, 12491, 14723, 42437, 57089, 58193, 61051, 63131, 63347, 64553, 64567, 64577, 64591, 64601, 64661, 64679, 64951, 65071, 65173, 65293, 65881, 66863, 69931, 79817, 99551, 129083, 165103, 263071, 284833, 1407647, 1515259, 4303027, 6440999, 14968819, 95517973, 527737957, 1893230839, 1950929941, 1964567161

Offset: 1

Jean-Marc Rebert, Apr 07 2023

Is this the same as A114924, or are there base-10 expressions of pi(p) which become p after striking 2 or more digits? - R. J. Mathar, Apr 18 2023

Chai Wah Wu, Table of n, a(n) for n = 1..54 (n=1..50 from Jean-Marc Rebert)

Cf. A362060.

from sympy import sieve
def okA362060(n):
    p = sieve[n]
    while n and p:
        if n%10 == p%10:
            n //= 10
        p //= 10
    return n == 0
print([sieve[k] for k in range(1, 10**6) if okA362060(k)]) # Michael S. Branicky, Apr 07 2023

from sympy import prime, nextprime
from itertools import count, islice
def A362066_gen(startvalue=1): # generator of terms >= startvalue
    p = prime(max(startvalue,1))
    for k in count(max(startvalue,1)):
        c = iter(str(p))
        if all(map(lambda b:any(map(lambda a:a==b,c)),str(k))):
            yield p
        p = nextprime(p)
A362066_list = list(islice(A362066_gen(),20)) # Chai Wah Wu, Apr 07 2023

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

A236469 Primes p such that pi(p) = floor(p/10), where pi is the prime counting function.

Original entry on oeis.org

64553, 64567, 64577, 64591, 64601, 64661

Offset: 1

K. D. Bajpai, Jan 26 2014

No further term below 32452843.
The first three terms in the sequence are consecutive primes.
Is this sequence finite?
No further term below 179424673.
The prime number theorem implies that this sequence is finite. Rosser proves that pi(x) < x/(log x - 4) for x >= 55, which can be used to show that there are no more terms. - Eric M. Schmidt, Aug 04 2014

J. B. Rosser. Explicit bounds for some functions of prime numbers. Amer. J. Math. 63 (1941), 211-232.

Cf. A075902, A114924, A067248.

KD := proc() local a,b; a:=ithprime(n); b:=floor(a/10); if n=b then RETURN (a);fi; end: seq(KD(), n=1..1000000);

Do[p = Prime[n]; k = Floor[p/10]; If[k == n, Print[p]], {n, 10^6}] (* Bajpai *)
Select[Prime[Range[6500]], PrimePi[#] == Floor[#/10] &] (* Alonso del Arte, Jan 26 2014 *)

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A362066 Primes associated with the indices in A362060.

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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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A236469 Primes p such that pi(p) = floor(p/10), where pi is the prime counting function.

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