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A287639 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has Hamming weight >= 10. 3

%I #13 Jun 18 2017 19:46:44

%S 1,1022,513,510,1025,766,257,1278,641,382,1153,638,385,1150,769,254,

%T 1281,702,321,1214,577,446,1089,830,193,1342,449,574,961,62,1473,318,

%U 705,1086,833,190,1345,670,353,1182,609,414,1121,798,225,1310,481,542,993,30

%N Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has Hamming weight >= 10.

%C Conjecturally, this is a permutation of the natural numbers.

%C This sequence has connections with A288139: here we have a lower bound, there an upper bound, on the Hamming weight of the sum of two consecutive terms.

%H Rémy Sigrist, <a href="/A287639/b287639.txt">Table of n, a(n) for n = 1..8192</a>

%H Rémy Sigrist, <a href="/A287639/a287639.gp.txt">PARI program for A287639</a>

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

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

%e -- ---- ----------- --------------

%e 1 1 1111111111 10

%e 2 1022 10111111111 10

%e 3 513 1111111111 10

%e 4 510 10111111111 10

%e 5 1025 11011111111 10

%e 6 766 1111111111 10

%e 7 257 10111111111 10

%e 8 1278 11101111111 10

%e 9 641 1111111111 10

%e 10 382 10111111111 10

%e 11 1153 11011111111 10

%e 12 638 1111111111 10

%e 13 385 10111111111 10

%e 14 1150 11101111111 10

%e 15 769 1111111111 10

%e 16 254 10111111111 10

%e 17 1281 11110111111 10

%e 18 702 1111111111 10

%e 19 321 10111111111 10

%e 20 1214 11011111111 10

%Y Cf. A000120, A288139.

%K nonn,look,base

%O 1,2

%A _Rémy Sigrist_, Jun 17 2017

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)