The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A295283 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A295283

a(n) = 1 + number of distinct earlier terms that have common one bits with n in binary representation.
(history; published version)

#17 by Bruno Berselli at Tue Nov 21 03:11:18 EST 2017

STATUS

reviewed

approved

#16 by Paolo P. Lava at Tue Nov 21 03:02:01 EST 2017

STATUS

proposed

reviewed

#15 by Rémy Sigrist at Tue Nov 21 01:12:23 EST 2017

STATUS

editing

proposed

#14 by Rémy Sigrist at Tue Nov 21 00:24:43 EST 2017

LINKS

Rémy Sigrist, <a href="/A295283/b295283.txt">Table of n, a(n) for n = 1..25000</a>

STATUS

approved

editing

Discussion

Tue Nov 21

01:12

Rémy Sigrist: added b-file

#13 by Susanna Cuyler at Mon Nov 20 22:08:39 EST 2017

STATUS

proposed

approved

#12 by Rémy Sigrist at Mon Nov 20 13:59:47 EST 2017

STATUS

editing

proposed

#11 by Rémy Sigrist at Mon Nov 20 13:59:24 EST 2017

COMMENTS

Empirically, this sequence and A295277 have tight connections:

- let c be the sequence defined for any n > 0 by c(n) = a(n) + A295277(n),

- we have for any n > 0, c(n) <= c(n+1) <= c(n) + 1,

- let u be the sequence defined for any n > 0 by u(n) = least k such that a(k) = n,

- let v be the sequence defined for any n >= 0 by v(n) = least k such that A295277(k) = n,

- we have for any n > 0, u(n) + 1 = v(n).

LINKS

Rémy Sigrist, <a href="/A295283/a295283_2.png">Scatterplot of (n, a(n) + A295277(n)) for n=1..2^20</a>

#10 by Rémy Sigrist at Mon Nov 20 13:39:51 EST 2017

LINKS

Rémy Sigrist, <a href="/A295283/a295283_1.png">Colored scatterplot of the first 2^20 terms</a> (where the color is function of min(A000120(a(n)),A000120((Max_{k=1..n-1} a(k))+2-a(n))))

CROSSREFS

Cf. A000120, A295277.

#9 by Rémy Sigrist at Sun Nov 19 15:22:31 EST 2017

FORMULA

a(2^n) = 0 for any n >= 0.

#8 by Rémy Sigrist at Sun Nov 19 15:19:45 EST 2017

PROG

(PARI) mx = 0; for (n=1, 85, v = 1 + sum(i=1, mx, bitand(i, n)!=0); print1 (v ", "); mx = max(mx, v))