A088754 Number of n-digit primes beginning with prime(n).

1, 2, 14, 107, 103, 851, 6931, 59557, 518971, 4585526, 41368791, 375232730, 3441863700, 31843327587, 295907384843, 2761221438054, 25890141962275, 244138314690159, 2306482418751769, 21874074143081175, 208132164249925671, 1983046852246630734, 18946883921641542673

Offset: 1

Author

Ray Chandler, Oct 15 2003

Keywords

• nonn
• base

Comments

Subsidiary sequence suggested in A088104.

Examples

			a(2) = 2 since 31 and 37 are the only two 2-digit primes beginning with prime(2) = 3.
		

Links

• Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Crossrefs

Cf. A077504, A077505, A088104, A088105, A088755.

Programs

PARI

A088754(n)={ local (resul,sdig,p,lo,hi) ; sdig=prime(n) ; lo=sdig ; hi=sdig+1 ; while( lo < 10^(n-1), lo *= 10 ; hi *= 10 ; ) ; resul=0 ; p=nextprime(lo) ; while(p < hi, resul++ ; p=nextprime(p+1) ; ) ; return(resul) ; }
{ for(n=1,11, print(A088754(n)); ) } \\ R. J. Mathar, Sep 25 2006

Python

from sympy import prime, primepi
def A088754(n):
    p = prime(n)
    m = n-len(str(p))
    return primepi((p+1)*10**m)-primepi(p*10**m) # Chai Wah Wu, Jun 18 2019

Extensions

a(10) from R. J. Mathar, Sep 25 2006

a(11)-a(14) from Floris P. van Doorn and Jasper Mulder (florisvandoorn(AT)hotmail.com), Oct 12 2009

a(15)-a(22) from Donovan Johnson, Apr 24 2013

a(23) from Chai Wah Wu, Jun 19 2019