A111311 Number of successive primes beginning with n at the first instance.

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

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: A265273 A341932 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