A138253 - OEIS

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A138253

Beatty discrepancy of the complementary equation b(n)=a(a(n))+n.

1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 1, 1 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,2`
	COMMENTS	`Consider the complementary equation b(n)=a(a(n))+n, with solutions` `a=A136495 and b=A136496; let r = lim a(n)/n and s = lim b(n)/n. The` `Beatty sequences of r and s are A138251 and A138252. We here introduce` `the notion of Beatty discrepancy of a complementary equation so that,` `in this case, it measures the closeness of the pair (A136495,A136496)` `to the Beatty pair (A138251,A138252).`
	FORMULA	`A138253(n) = d(n)-c(c(n))-n, where c(n)=A138251(n), d(n)=A138252(n).`
	EXAMPLE	`d(1)-c(c(1))-1=3-1-1=1;` `d(2)-c(c(2))-2=6-2-2=2;` `d(3)-c(c(3))-3=9-5-3=1;` `d(4)-c(c(4))-4=12-7-4=1.`
	CROSSREFS	`Cf. A136495, A136496, A138251, A138252.` `Sequence in context: A142598 A037800 A144411 * A085737 A191904 A005090` `Adjacent sequences: A138250 A138251 A138252 * A138254 A138255 A138256`
	KEYWORD	`nonn`
	AUTHOR	`Clark Kimberling (ck6(AT)evansville.edu), Mar 09 2008`

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Last modified February 14 23:16 EST 2012. Contains 205687 sequences.