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A093641 Numbers of form 2^i * prime(j), i>=0, j>0, together with 1. 15
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 47, 48, 52, 53, 56, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 86, 88, 89, 92, 94, 96, 97, 101, 103, 104, 106, 107, 109, 112 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is either 1, prime, or of form 2a(m), m<n.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a001227(a(n)) <= 2. - Reinhard Zumkeller, May 01 2012

Number A(x) of a(n) not exceeding x equals 1 + pi(x) + pi(x/2) + pi(x/4) + ..., where pi(x) is the number of primes <= x. If x goes to infinity, A(x)~2*x/log(x) and a(n)~n*log(n)/2 (n-->infinity). - Vladimir Shevelev, Feb 06 2014

EXAMPLE

55 is not a member, as 5*11 is not of the form 2^i * prime.

PROG

(PARI) upTo(lim)=my(v=List([1])); for(e=0, log(lim)\log(2), forprime(p=2, lim>>e, listput(v, p<<e))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Aug 21 2011

(Haskell)

a093641 n = a093641_list !! (n-1)

a093641_list = filter ((<= 2) . a001227) [1..]

-- Reinhard Zumkeller, May 01 2012

CROSSREFS

A093640(a(n)) = A000005(a(n)); A000040 and A000079 are subsequences.

A105440 is a subsequence, see also A105442. - Reinhard Zumkeller, Apr 09 2005

Cf. A078822, A007088.

Complement of A105441; A001221(a(n))<=2; A005087(a(n))<=1; A087436(a(n))<=1.

See also A105442.

Union of A038550 and A000079, see also A008578.

Sequence in context: A207674 A162722 A123345 * A209638 A191844 A096157

Adjacent sequences:  A093638 A093639 A093640 * A093642 A093643 A093644

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Apr 07 2004

STATUS

approved

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Last modified February 19 18:31 EST 2018. Contains 299356 sequences. (Running on oeis4.)