

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
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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(n1) < 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



