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A088754 Number of n-digit primes beginning with prime(n). 6
1, 2, 14, 107, 103, 851, 6931, 59557, 518971, 4585526, 41368791, 375232730, 3441863700, 31843327587, 295907384843, 2761221438054, 25890141962275, 244138314690159, 2306482418751769, 21874074143081175, 208132164249925671, 1983046852246630734, 18946883921641542673 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Subsidiary sequence suggested in A088104.

LINKS

Table of n, a(n) for n=1..23.

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

EXAMPLE

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

PROG

(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

CROSSREFS

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

Sequence in context: A051708 A074618 A108436 * A103945 A111713 A144278

Adjacent sequences:  A088751 A088752 A088753 * A088755 A088756 A088757

KEYWORD

nonn,base

AUTHOR

Ray Chandler, Oct 15 2003

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

STATUS

approved

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Last modified August 25 03:10 EDT 2019. Contains 326318 sequences. (Running on oeis4.)