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Search: id:A111311
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| A111311 |
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Number of successive primes beginning with n at the first instance. |
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+0
1
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 subsidiery sequence.
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EXAMPLE
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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.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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CROSSREFS
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Sequence in context: A143441 A016527 A010325 this_sequence A016524 A087963 A010323
Adjacent sequences: A111308 A111309 A111310 this_sequence A111312 A111313 A111314
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 11 2005
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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