id:A055778 - OEIS Search Results

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Number of 1's in base phi representation of n.

+0
7

0, 1, 2, 2, 3, 3, 3, 2, 3, 4, 4, 5, 4, 4, 4, 5, 4, 4, 2, 3, 4, 4, 5, 5, 5, 4, 5, 6, 6, 7, 5, 5, 5, 6, 5, 5, 4, 5, 6, 6, 7, 5, 5, 5, 6, 5, 5, 2, 3, 4, 4, 5, 5, 5, 4, 5, 6, 6, 7, 6, 6, 6, 7, 6, 6, 4, 5, 6, 6, 7, 7, 7, 6, 7, 8, 8, 9, 6, 6, 6, 7, 6, 6, 5, 6, 7, 7, 8, 6, 6, 6, 7, 6, 6, 4, 5, 6, 6, 7, 7, 7, 6, 7, 8, 8 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`Uses greedy algorithm (start with largest possible power of phi, then work downward)` `constant (float): phi=(sqrt(5)+1)/2; function: lphi(x)=log(x)/log(phi); variable (float): rem=n; variable (integer): count=0; loop: while rem>0 {rem=rem-phi^floor[lphi(x)]; count++;} result: return count;`
	LINKS	`R. Knott, iUsing Powers of Phi to represent Integers (Base Phi) (inspiration for this sequence).` `Eric Weisstein's World of Mathematics, Phi Number System`
	EXAMPLE	`4 in base phi is 101.01, which has three 1's.`
	CROSSREFS	`Sequence in context: A059253 A108133 A014499 this_sequence A106482 A122462 A165024` `Adjacent sequences: A055775 A055776 A055777 this_sequence A055779 A055780 A055781`
	KEYWORD	`base,easy,nonn`
	AUTHOR	`Robert Lozyniak (11(AT)onna.com), Jul 12 2000`
	EXTENSIONS	`More terms and algorithm from Henry Bottomley (se16(AT)btinternet.com), Aug 04 2000`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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