The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A288139 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A288139

Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has Hamming weight <= 4.
(history; published version)

#13 by N. J. A. Sloane at Sun Jun 18 19:46:52 EDT 2017

STATUS

proposed

approved

#12 by Rémy Sigrist at Sun Jun 18 13:34:56 EDT 2017

STATUS

editing

proposed

#11 by Rémy Sigrist at Sun Jun 18 13:34:06 EDT 2017

EXAMPLE

The first terms, alongside a(n)+a(n+1) in binary and its Hamming weight are:

#10 by Rémy Sigrist at Sun Jun 18 13:33:10 EDT 2017

COMMENTS

This sequence has connections with A287639: here we have an upper bound, there a lower bound, on the Hamming weight of the sum of two consecutive terms.

LINKS

Rémy Sigrist, <a href="/A288139/b288139.txt">Table of n, a(n) for n = 1..16384</a>

Rémy Sigrist, <a href="/A288139/a288139.gp.txt">PARI program for A288139</a>

EXAMPLE

The first terms, alongside a(n)+a(n+1) and its Hamming weight are:

n a(n) a(n)+a(n+1) Hamming weight

-- ---- ----------- --------------

1 1 11 2

2 2 101 2

3 3 111 3

4 4 1001 2

5 5 1011 3

6 6 1101 3

7 7 1111 4

8 8 10001 2

9 9 10011 3

10 10 10101 3

11 11 10111 4

12 12 11001 3

13 13 11011 4

14 14 11101 4

15 15 100000 1

16 17 100001 2

17 16 100010 2

18 18 100101 3

19 19 100111 4

20 20 101001 3

CROSSREFS

Cf. A000120, A287639.

#9 by Rémy Sigrist at Sat Jun 17 09:58:15 EDT 2017

NAME

allocated for Rémy Sigrist

Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has Hamming weight <= 4.

DATA

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 19, 20, 21, 22, 23, 25, 24, 26, 27, 29, 28, 30, 34, 31, 33, 32, 35, 36, 37, 38, 39, 41, 40, 42, 43, 45, 44, 46, 50, 47, 49, 48, 51, 53, 52, 54, 58, 55, 57, 56, 60, 68, 61, 59, 69, 62, 66, 63, 65

OFFSET

1,2

COMMENTS

Conjecturally, this is a permutation of the natural numbers.

KEYWORD

allocated

nonn,look,base

AUTHOR

Rémy Sigrist, Jun 17 2017

STATUS

approved

editing

#8 by Rémy Sigrist at Sat Jun 17 09:58:15 EDT 2017

NAME

allocated for Rémy Sigrist

KEYWORD

recycled

allocated

#7 by Joerg Arndt at Sat Jun 17 09:27:48 EDT 2017

STATUS

reviewed

approved

#6 by Michel Marcus at Sat Jun 17 03:53:39 EDT 2017

STATUS

proposed

reviewed

#5 by Joerg Arndt at Sat Jun 17 02:37:04 EDT 2017

STATUS

editing

proposed

#4 by Joerg Arndt at Sat Jun 17 02:37:00 EDT 2017

NAME

Mersenne primes minus 1.

DATA

6, 30, 126, 8190, 131070, 524286, 2147483646, 2305843009213693950, 618970019642690137449562110, 162259276829213363391578010288126, 170141183460469231731687303715884105726

OFFSET

1,1

COMMENTS

Every perfect number (n)>6 have A000668(n)-1 different sequences, where the center of every sequence is a multiple of it's proper superperfect number.

FORMULA

A000668(n)-1, for n>3.

EXAMPLE

Perfect number=28;Mersenne prime=7;7-1=6

1+2+3+4+5+6+7=28;28/28=1

5+6+7+8+9+10+11=56;56/28=2

9+10+11+12+13+14+15=84;84/28=3

13+14+15+16+17+18+19=112;112/28=4

17+18+19+20+21+22+23=140;140/28=5

21+22+23+24+25+26+27=168;168/28=6

KEYWORD

nonn,changed

recycled

AUTHOR

César Aguilera, Jun 05 2017