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A111311 Number of successive primes beginning with n at the first instance. 1
4, 1, 1, 3, 1, 2, 1, 2, 1, 4, 1, 1, 1, 1, 2, 2, 1, 1, 1, 14, 1, 3, 1, 1, 2, 2, 2, 2, 1, 1, 1, 11, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 11, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 13, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 4, 1, 8, 3, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(p) = 1. If a composite n has k digits and there is no prime beginning with n of k+1 digits then a(n) shoots up and a(n-1) < a(n) > a(n+1). a(n) must exceed n at some values of n. as a(20) = 14, etc. at what point a(n) exceeds n? and we get a subsidiary sequence.

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

a(1) = 4 as there are four primes 11,13,17,19, that begin with 1.

a(2) = 1 as 2 follows by 3 hence 23 is not considered for a count.

a(20) = 14, 14 primes from 2003 to 2099.

MAPLE

A111311 := proc(n) local p, nstrt, a ; if isprime(n) then 1; else nstrt := 10 ; a := 0 ; while a = 0 do for p from nstrt*n to nstrt*n+nstrt -1 do if isprime(p) then a := a+1 ; fi ; od ; if a <> 0 then RETURN(a) ; fi ; nstrt := nstrt*10 ; od: fi ; end: seq(A111311(n), n=1..100) ; # R. J. Mathar, Feb 08 2008

CROSSREFS

Sequence in context: A010325 A265273 A293770 * A327893 A326410 A255235

Adjacent sequences:  A111308 A111309 A111310 * A111312 A111313 A111314

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Nov 11 2005

EXTENSIONS

Corrected and extended by R. J. Mathar, Feb 08 2008

STATUS

approved

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)