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.

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

Offset: 1

Author

Labos Elemer, Jul 29 2003

Keywords

• nonn

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)

Examples

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

Links

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

Crossrefs

Cf. A031930, A031931, A046133.

Programs

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}]]
PrimePi[#+11]-PrimePi[#+1]&/@Select[Prime[Range[400]],PrimeQ[#+12]&] (* Harvey P. Dale, Jul 30 2022 *)

Extensions

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