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A101288 The number of primes between the n-th isolated prime and n-th 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 (list; graph; refs; listen; history; text; internal format)
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 x-1 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(n-1)+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(n-2) ; 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](a7510-1)-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

Juri-Stepan 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

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Last modified May 19 17:48 EDT 2019. Contains 323395 sequences. (Running on oeis4.)