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A088754
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Number of n-digit primes beginning with prime(n).
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6
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1, 2, 14, 107, 103, 851, 6931, 59557, 518971, 4585526, 41368791, 375232730, 3441863700, 31843327587, 295907384843, 2761221438054, 25890141962275, 244138314690159, 2306482418751769, 21874074143081175, 208132164249925671, 1983046852246630734, 18946883921641542673
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OFFSET
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1,2
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COMMENTS
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Subsidiary sequence suggested in A088104.
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LINKS
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Table of n, a(n) for n=1..23.
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)
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EXAMPLE
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a(2) = 2 since 31 and 37 are the only two 2-digit primes beginning with prime(2) = 3.
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PROG
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(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
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CROSSREFS
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Cf. A077504, A077505, A088104, A088105, A088755.
Sequence in context: A051708 A074618 A108436 * A103945 A111713 A144278
Adjacent sequences: A088751 A088752 A088753 * A088755 A088756 A088757
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KEYWORD
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nonn,base
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AUTHOR
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Ray Chandler, Oct 15 2003
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EXTENSIONS
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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
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STATUS
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approved
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