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 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

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