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A116127
Number of numbers that are congruent to {2, 4} mod 6 between prime(n) and prime(n+1) inclusive.
3
1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 4, 2, 2, 0, 4, 0, 2, 2, 2, 2, 2, 0, 4, 0, 2, 0, 4, 4, 2, 0, 2, 2, 0, 4, 2, 2, 2, 0, 2, 2, 0, 4, 4, 2, 0, 2, 4, 2, 4, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 0, 4, 0, 2, 2, 2, 2, 2, 0, 2, 4, 2, 2, 2, 2, 2, 4, 0, 6, 2, 4, 2, 2, 0, 2
OFFSET
1,4
COMMENTS
For n > 2,
A001223(n) = 2 iff a(n) = 0,
A001223(n) = 4 or 6 or 8 iff a(n) = 2,
A001223(n) = 10 or 12 or 14 iff a(n) = 4,
A001223(n) = 16 or 18 or 20 iff a(n) = 6,
and so on. This can be generalized to
A001223(n) = 3*k-2 or 3*k or 3*k+2 iff a(n) = k for k >= 2.
LINKS
MAPLE
P:= select(isprime, [seq(i, i=5..1000, 2)]):
Delta:= P[2..-1]-P[1..-2]:
f:= t -> (t + 2*(t+1 mod 3) - 2)/3:
1, 1, op(map(f, Delta)); # Robert Israel, Jun 19 2019
MATHEMATICA
s={}; Do[c=0; Do[If[MemberQ[{2, 4}, Mod[i, 6]], c=c+1], {i, Prime[n], Prime[n+1]}]; AppendTo[s, c], {n, 105}]; s (* James C. McMahon, Aug 18 2024 *)
PROG
(Magma) [ #[ k: k in [NthPrime(n)..NthPrime(n+1)] | r eq 2 or r eq 4 where r is k mod 6 ]: n in [1..105] ]; /* Klaus Brockhaus, Apr 15 2007 */
CROSSREFS
Cf. A000040 (primes), A001223 (differences between consecutive primes), A047235 (numbers congruent to {2, 4} mod 6), A002654.
Sequence in context: A029225 A341977 A309937 * A039979 A204173 A103668
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Apr 08 2007
EXTENSIONS
Edited, corrected and extended by Klaus Brockhaus, Apr 15 2007
STATUS
approved