A213902 Number of integers of the form 6*k+1 and 6*k-1 between prime(n) and prime(n+1).

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 4, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 0, 2, 0, 0, 0, 3, 3, 0, 0, 0, 1, 0, 2, 1, 1, 1, 0, 1, 0, 0, 2, 4, 0, 0, 0, 4, 1, 2, 0, 0, 1, 2, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 0, 1, 0, 1, 2

Offset

1,24

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

nn = 100; t = Join[{3}, Union[6*Range[nn] - 1, 6*Range[nn] + 1]]; cnt = 0; t2 = {}; Do[If[PrimeQ[t[[i]]], AppendTo[t2, cnt]; cnt = 0, cnt++], {i, Length[t]}]; t2 (* T. D. Noe, Jun 26 2012 *)
Module[{nn=90, k61}, k61=Flatten[#+{1, 5}&/@(6Range[0, Prime[nn+1]])]; Table[ Count[ k61, _?(Prime[n]<#<Prime[n+1]&)], {n, nn}]] (* Harvey P. Dale, Mar 11 2019 *)

Prog

(Python)
# primes=[2, 3, 5, 7, 11, 13, 17, ...]
for i in range(777):
    prime = primes[i]
    nextp = primes[i+1]
    k = nextp//6 - prime//6
    if k:
        k = (k-1)*2 + (prime%6==1) + (nextp%6==5)
    print(str(k), end=', ')

Crossrefs

Cf. A001223.

Sequence in context: A005929 A005871 A005888 * A170770 A107499 A123298

Adjacent sequences: A213899 A213900 A213901 * A213903 A213904 A213905

Keyword

nonn,easy

Author

Alex Ratushnyak, Jun 24 2012

Status

approved