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A343501 Positions of 4's in A003324. 6
4, 6, 14, 16, 20, 22, 24, 30, 36, 38, 46, 52, 54, 56, 62, 64, 68, 70, 78, 80, 84, 86, 88, 94, 96, 100, 102, 110, 116, 118, 120, 126, 132, 134, 142, 144, 148, 150, 152, 158, 164, 166, 174, 180, 182, 184, 190, 196, 198, 206, 208, 212, 214, 216, 222, 224, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers of the form (2*k+1) * 2^e where e >= 1, k+e is even. In other words, union of {(4*m+1) * 2^(2t)} and {(4*m+3) * 2^(2t-1)}, where m >= 0, t > 0.

Numbers whose quaternary (base-4) expansion ends in 100...00 or 1200..00 or 3200..00. At least one trailing zero is required in the first case but not in the latter two cases.

There are precisely 2^(N-2) terms <= 2^N for every N >= 2.

Also even indices of 1 in A209615. - Jianing Song, Apr 24 2021

Complement of A343500 with respect to the even numbers. - Jianing Song, Apr 26 2021

LINKS

Jianing Song, Table of n, a(n) for n = 1..16384 (all terms <= 2^16).

FORMULA

a(n) = 2*A338691(n). - Hugo Pfoertner, Apr 26 2021

EXAMPLE

A003324 starts with 1, 2, 3, 4, 1, 4, 3, 2, 1, 2, 3, 2, 1, 4, 3, 4, ... We have A003324(4) = A003324(6) = A003324(14) = A003324(16) = ... = 4, so this sequence starts with 4, 6, 14, 16, ...

MATHEMATICA

okQ[n_] := If[OddQ[n], False, Module[{e = IntegerExponent[n, 2], k}, k = (n/2^e - 1)/2; EvenQ[k + e]]];

Select[Range[1000], okQ] (* Jean-Fran├žois Alcover, Apr 19 2021, after PARI *)

PROG

(PARI) isA343501(n) = if(n%2, 0, my(e=valuation(n, 2), k=bittest(n, e+1)); !((k+e)%2))

CROSSREFS

Cf. A003324, A343500 (positions of 2's), A209615, A338691.

Even terms in A338692.

Sequence in context: A102029 A310618 A310619 * A029641 A089377 A310620

Adjacent sequences:  A343498 A343499 A343500 * A343502 A343503 A343504

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Apr 17 2021

STATUS

approved

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Last modified September 27 21:12 EDT 2021. Contains 347698 sequences. (Running on oeis4.)