A180055 In binary expansion, number of 1's in 5n is less than in n.

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

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: A037974 A318957 A356064 * A371463 A346003 A164007

Adjacent sequences: A180052 A180053 A180054 * A180056 A180057 A180058

Keyword

base,nonn

Author

Zak Seidov, Aug 08 2010

Status

approved