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A130328 Triangle of differences between powers of 2, read by rows. 5
1, 3, 2, 7, 6, 4, 15, 14, 12, 8, 31, 30, 28, 24, 16, 63, 62, 60, 56, 48, 32, 127, 126, 124, 120, 112, 96, 64, 255, 254, 252, 248, 240, 224, 192, 128, 511, 510, 508, 504, 496, 480, 448, 384, 256 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A130321 * A059268 as infinite lower triangular matrices.
Row sums = A000337: (1, 5, 17, 49, 129, 321, ...). A130329 = A059268 * A130321.
From Alonso del Arte, Mar 13 2008: (Start)
Column 0 contains the Mersenne numbers A000225.
Column 1 is A000918.
An even perfect number (A000396) is found in the triangle by reference to its matching exponent for the Mersenne prime p (A000043) thus: go to row 2p - 1 and then column p - 1 (remembering that the first position is column 0).
Likewise divisors of multiply perfect numbers, if not the multiply perfect numbers themselves, can also be found in this triangle. (End)
LINKS
FORMULA
t(n, k) = 2^n - 2^k, where n is the row number and k is the column number, running from 0 to n - 1. (If k is allowed to reach n, then the triangle would have an extra diagonal filled with zeros) - Alonso del Arte, Mar 13 2008
EXAMPLE
First few rows of the triangle are;
1;
3, 2;
7, 6, 4;
15, 14, 12, 8;
31, 30, 28, 24, 16;
63, 62, 60, 56, 48, 32;
...
a(5, 2) = 28 because 2^5 = 32, 2^2 = 4 and 32 - 4 = 28.
MATHEMATICA
ColumnForm[Table[2^n - 2^k, {n, 15}, {k, 0, n - 1}], Center] (* Alonso del Arte, Mar 13 2008 *)
CROSSREFS
Sequence in context: A072764 A364832 A349890 * A228993 A083569 A071574
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, May 24 2007
EXTENSIONS
Better definition from Alonso del Arte, Mar 13 2008
STATUS
approved

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Last modified April 13 03:15 EDT 2024. Contains 371639 sequences. (Running on oeis4.)