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A270190 Numbers n for which prime(n+1)-prime(n) is a multiple of three. 12
9, 11, 15, 16, 18, 21, 23, 32, 36, 37, 39, 40, 46, 47, 51, 54, 55, 56, 58, 67, 71, 73, 74, 76, 84, 86, 91, 96, 97, 99, 100, 102, 103, 105, 107, 108, 110, 111, 114, 118, 119, 121, 123, 129, 130, 133, 139, 160, 161, 164, 165, 167, 168, 170, 174, 179, 180, 184, 185, 187, 188, 194, 195, 197, 199, 200, 202, 203, 205, 208, 210 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers n for which A001223(n) = 0 modulo 3.
See comments in A270189 and A269364.
Equivalently, numbers n for which prime(n+1)-prime(n) is a multiple of six. See A276414 for runs of increasing length of consecutive integers. - M. F. Hasler, Sep 03 2016
LINKS
Terence Tao, Biases between consecutive primes, blog entry March 14, 2016
FORMULA
Other identities. For all n >= 1:
a(n) = A269399(n) + 6.
A269850(a(n)) = n.
EXAMPLE
9 is present as the difference between A000040(9+1) = 29 and A000040(9) = 23 is 6, a multiple of three.
MATHEMATICA
Select[Range@ 210, Divisible[Prime[# + 1] - Prime@ #, 3] &] (* Michael De Vlieger, Mar 17 2016 *)
PrimePi/@Select[Partition[Prime[Range[350]], 2, 1], Divisible[#[[2]]-#[[1]], 3]&][[All, 1]] (* Harvey P. Dale, Jul 11 2017 *)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A270190 (ZERO-POS 1 1 A137264))
(PARI) isok(n) = ((prime(n+1) - prime(n)) % 3) == 0; \\ Michel Marcus, Mar 17 2016
CROSSREFS
Complement: A270189.
Positions of zeros in A137264.
Left inverse: A269850.
Sequence in context: A101754 A348614 A113339 * A320701 A287340 A037009
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 16 2016
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)