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A180055 In binary expansion, number of 1's in 5n is less than in n. 2
13, 26, 29, 52, 53, 55, 58, 61, 77, 103, 104, 106, 109, 110, 111, 116, 117, 119, 122, 125, 154, 157, 205, 206, 207, 208, 212, 213, 215, 218, 219, 220, 221, 222, 223, 231, 232, 234, 237, 238, 239, 244, 245, 247, 250, 253, 308, 309, 311, 314, 317, 333, 359, 365 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Or, binary weight of 5n is less than binary weight of n.

Also called the 5-flimsy numbers; see the Stolarsky reference.

If m is here, 2m is too. Hence the "primitive solutions" are all odd ones:

13,29,53,55,61,77,103,109,111,117,119,125,157,205,207,213,215,219,221,223,231.

LINKS

Table of n, a(n) for n=1..54.

Kenneth B. Stolarsky, Integers whose multiples have anomalous digital frequencies, Acta Arithmetica 38 (2) (1980), 117-128.

FORMULA

A000120(n) > A000120(5n).

MATHEMATICA

Select[Range[1000], Count[IntegerDigits[5#, 2], 1]<Count[IntegerDigits[ #, 2], 1]&]

PROG

(PARI) for(k=1, 370, if(hammingweight(5*k) < hammingweight(k), print1(k, ", "))) \\ Hugo Pfoertner, Dec 27 2019

CROSSREFS

Cf. A000120, A005360, A180054.

Sequence in context: A095781 A037974 A318957 * A346003 A164007 A101870

Adjacent sequences:  A180052 A180053 A180054 * A180056 A180057 A180058

KEYWORD

base,nonn

AUTHOR

Zak Seidov, Aug 08 2010

STATUS

approved

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Last modified January 28 12:46 EST 2022. Contains 350656 sequences. (Running on oeis4.)