login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086139 Let p = A046133(n), that is, let p run through the list of primes such that p+12 is also prime (A046133); a(n) = number of primes in the interval p + 1 through p + 11 inclusive. 2
3, 3, 3, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 3, 3, 2, 1, 1, 1, 1, 1, 1, 0, 0, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 2, 0, 1, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 1, 2, 1, 2, 0, 1, 3, 2, 0, 0, 0, 1, 1, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Michael De Vlieger, Jul 30 2017: (Start)

a(n) = 0 for n = {24, 25, 44, 48, 53, 57, 62, 70, 82, 84, 89, 94, ...}.

a(n) = 1 for n = {9, 14, 18, 19, 20, 21, 22, 23, 28, 29, 30, 33, ...}.

a(n) = 2 for n = {4, 5, 6, 7, 8, 10, 11, 12, 13, 17, 26, 27, 31, ...}.

a(n) = 3 for n = {1, 2, 3, 15, 16, 96, 118, 183, 266, 570, 581, ...}.

(End)

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

EXAMPLE

For n=1, we have p=5, the primes between 5 and 5+12=17 are 7,11,13, so a(1)=3.

MAPLE

a:=[]; b:=[];

for n from 1 to 200 do if isprime(ithprime(n)+12) then

   a:=[op(a), ithprime(n)];

c:=0;

for i from 1 to 11 do if isprime(ithprime(n)+i) then c:=c+1; fi; od;

b:=[op(b), c];

fi;

od:

a; # A046133b; # this sequence

MATHEMATICA

cp[x_, y_] := Count[Table[PrimeQ[i], {i, x, y}], True]; d = 12; Do[s = Prime[n]; If[PrimeQ[s+d], Print[cp[s+1, s+d-1]]], {n, 1, 1000}]

(* Second program: *)

With[{d = 12}, DeleteCases[#, -1] &@ Table[Function[p, If[PrimeQ[p + d],

Count[Range[p + 1, p + d - 1], _?PrimeQ], -1] ]@ Prime@ n, {n, 252}]]

CROSSREFS

Cf. A031930, A031931, A046133.

Sequence in context: A136218 A112106 A010608 * A237879 A074804 A242465

Adjacent sequences:  A086136 A086137 A086138 * A086140 A086141 A086142

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 29 2003

EXTENSIONS

Definition edited by N. J. A. Sloane, Aug 05 2017 following analysis by Michael De Vlieger, Jul 30 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 27 00:45 EST 2021. Contains 340443 sequences. (Running on oeis4.)