A076890 Number of primes up to n-th palindromic number.

0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 8, 11, 14, 16, 18, 21, 23, 25, 26, 29, 30, 32, 34, 36, 37, 39, 42, 43, 46, 47, 47, 50, 53, 54, 55, 58, 60, 61, 62, 65, 66, 67, 68, 71, 72, 74, 76, 77, 79, 80, 82, 84, 86, 87, 90, 91, 92, 94, 96, 97, 99, 99, 100, 101, 103, 105, 106, 108, 110, 112

Offset

1,3

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = A000720(A002113(n)). - Michel Marcus, Jun 14 2024

Example

a(11)=8 because there are 8 primes up to 11th palindromic number (i.e. 22).

Prog

(Python)
from sympy import primepi
def A076890(n):
    if n == 1: return 0
    y = 10*(x:=10**(len(str(n+1>>1))-1))
    return primepi((c:=n+1-x)*x+int(str(c)[-2::-1]or 0) if n<x+y else (c:=n+1-y)*y+int(str(c)[-1::-1]or 0)) # Chai Wah Wu, Jun 14 2024

Crossrefs

Cf. A000720, A002113.

Sequence in context: A028825 A326492 A132924 * A103358 A063084 A127079

Adjacent sequences: A076887 A076888 A076889 * A076891 A076892 A076893

Keyword

base,nonn

Author

Shyam Sunder Gupta, Nov 25 2002

Status

approved