

A169969


Locations of row maxima in "crushed" version of Stern's diatomic array.


0



1, 3, 5, 7, 11, 13, 21, 27, 43, 53, 85, 107, 171, 213, 341, 427, 683, 853, 1365, 1707, 2731, 3413, 5461, 6827, 10923, 13653, 21845, 27307, 43691, 54613, 87381, 109227, 174763, 218453, 349525, 436907, 699051, 873813, 1398101, 1747627, 2796203, 3495253
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OFFSET

1,2


COMMENTS

From Michel Marcus, Jan 22 2015: (Start)
The Stern's diatomic array begins (see A049456).
1...............................1
1...............2...............1
1.......3.......2.......3.......1
1...4...3...5...2...5...3...4...1
1.5.4.7.3.8.5.7.2.7.5.8.3.7.4.5.1
...
The "crushed" version is obtained by removing the right column, and then squeezing everything to the left.
1;
1, 2;
1, 3, 2, 3;
1, 4, 3, 5, 2, 5, 3, 4;
1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5;
...
This gives sequence 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, ... (cf. A002487).
The "crushed" array row maxima are: 1, 2, 3, 5, 8, ... (cf. A000045).
The indices of these values in A002487 are 1, 3, 5, 7, 11, ... : this sequence.
Note, for instance, that for 3rd row, the maximum which is 3, appears twice, at indices 5 and 7, giving 2 terms for this sequence.
(End)


LINKS

Table of n, a(n) for n=1..42.
S. Northshield, Stern's diatomic sequence 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, ..., Amer. Math. Monthly, 117 (2010), 581598.


PROG

(PARI) fusc(n)=local(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); b; \\ from A002487
lista(nn) = {nb = 2^(nn+1)1; vall = vector(nb, n, fusc(n)); for (n=1, nn, vmax = 0; for (j=2^(n1), 2^n1, if (vall[j] > vmax, vmax = vall[j]); ); for (j=2^(n1), 2^n1, if (vall[j] == vmax, print1(j, ", ")); ); ); } \\ Michel Marcus, Jan 22 2015


CROSSREFS

Sequence in context: A249077 A126960 A119753 * A174350 A240476 A040140
Adjacent sequences: A169966 A169967 A169968 * A169970 A169971 A169972


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Aug 08 2010


EXTENSIONS

More terms from Michel Marcus, Jan 22 2015


STATUS

approved



