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A139123 Successive sequences whose numbers and their differences of increasing rank include all numbers (generalization of A005228). 0
1, 1, 3, 1, 3, 7, 12, 1, 3, 7, 15, 18, 1, 3, 7, 15, 28, 26, 1, 3, 7, 15, 31, 47, 35, 1, 3, 7, 15, 31, 60, 74, 45, 1, 3, 7, 15, 31, 63, 108, 110, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The condition 2) imposes for any k 2 and 4 afor values of the two first k-th difference and hence 2^1 to 2^(1+k) for the (1+k) first differences and finally (2^n)-1 for values of k(n){n;1;k+2).

In conclusion, in the limit, the terms of the sequence r(k) will be when k tends to infinity = inf(n) = (2^n) -1 (1,3,7,15,31,63,127,255,511,. . . ).

LINKS

Table of n, a(n) for n=0..41.

EXAMPLE

Construct the following array where the sequence k(n) of the k-th row is the unique one 1) whose numbers and their k-th differences include exactly all numbers once 2) where both of the sequence and the sequence of their k-th differences are increasing

1 3 7 12 18 26 35 45 56 69 83

1 3 7 15 28 47 74 110 156 213 282 . . .

1 3 7 15 31 60 108 183 294 451 665 . . .

1 3 7 15 31 63 124 233 417 712 1164 . . .

1 3 7 15 31 63 127 252 486 904 1617 . . .

a(n) are the terms of this array read by antidiagonals.

Of course, the first row is A005228.

CROSSREFS

Cf. A005228.

Sequence in context: A086401 A095732 A001644 * A133580 A019603 A171843

Adjacent sequences:  A139120 A139121 A139122 * A139124 A139125 A139126

KEYWORD

easy,nonn,uned

AUTHOR

Philippe Lallouet (philip.lallouet(AT)orange.fr), Jun 05 2008

STATUS

approved

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Last modified June 27 15:05 EDT 2017. Contains 288790 sequences.