

A101288


The number of primes between the nth isolated prime and nth isolated composite.


1



1, 5, 6, 7, 5, 5, 4, 2, 2, 3, 3, 4, 9, 6, 7, 10, 12, 10, 12, 13, 15, 26, 27, 30, 36, 41, 43, 46, 48, 49, 68, 69, 70, 73, 76, 94, 95, 97, 98, 97, 104, 114, 118, 118, 120, 122, 131, 135, 138, 139, 153, 155, 160, 162, 162, 170, 178, 177, 182, 181, 184, 188, 191, 192, 194
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OFFSET

1,2


COMMENTS

Instead of "isolated" one speaks also of "single" primes, they are listed in A007510 and include 2 by convention. By isolated composites are meant composites whose two neighbors both are prime, i.e., the averages of twin primes, A014574.  M. F. Hasler, Aug 11 2015


LINKS

Table of n, a(n) for n=1..65.


EXAMPLE

a(1) = 1 = # { 3 }, the only prime between 2 (the first "isolated prime" according to A007510) and 4, the first "isolated composite" in the sense that x1 and x+1 both are primes.
a(2) = 5 = # { 7, 11, 13, 17, 19 }, the primes between the second isolated prime, 23, and second isolated composite, 6.
a(3) = 6 = # { 31, 29, 23, 19, 17, 13 }, the primes between A007510(3) = 37 and A014574(3) = 12.


MAPLE

From R. J. Mathar, Apr 25 2010: (Start)
A007510 := proc(n) if n = 1 then 2; else for a from procname(n1)+1 do if isA007510(a) then return a; end if; end do; end if; end proc:
isA007510 := proc(n) isprime(n) and not isprime(n+2) and not isprime(n2) ; simplify(%) ; end proc:
A101288 := proc(n) if n = 1 then return 1 ; end if; a7510 := A007510(n) ; a4574 := A014574(n) ; if a7510 > a4574 then numtheory[pi](a75101)numtheory[pi](a4574) ; else numtheory[pi](a4574)numtheory[pi](a7510+1) ; end if; end proc:
seq(A101288(n), n=1..120) ; (End)


CROSSREFS

Cf. A000040, A007510, A014574.
Sequence in context: A021642 A299082 A171423 * A212479 A095942 A139395
Adjacent sequences: A101285 A101286 A101287 * A101289 A101290 A101291


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Nov 02 2009


EXTENSIONS

More terms from R. J. Mathar, Apr 25 2010
Edited by Jon E. Schoenfield and M. F. Hasler, Aug 11 2015


STATUS

approved



