|
Search: id:A075325
|
|
|
| A075325 |
|
Pair the natural numbers such that the m-th pair is (r, s) where r, s and s-r are the smallest numbers which have not occurred earlier and also are not equal to the difference of any earlier pair: (1, 3), (4, 9), (6, 13), (8, 18), (11, 23), (14, 29), (16, 33), (19, 39), (21, 43), (24, 49), (26, 53), (28, 58), ... Sequence gives first term of each pair. |
|
+0
4
|
|
| 1, 4, 6, 8, 11, 14, 16, 19, 21, 24, 26, 28, 31, 34, 36, 38, 41, 44, 46, 48, 51, 54, 56, 59, 61, 64, 66, 68, 71, 74, 76, 79, 81, 84, 86, 88, 91, 94, 96, 99, 101, 104, 106, 108, 111, 114, 116, 118, 121, 124, 126, 128, 131, 134, 136, 139, 141, 144, 146, 148, 151, 154, 156
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Most of the pairs are of the form (r,2r+1) except for the ones like a(4) = (8,18) and a(12) = (28,58) and (38,78) etc. which are of the form (r,2r +2).
|
|
FORMULA
|
Let A(n) = A007814(n). Let B(n) = A(n) + 1 if A(n) < 2; B(n) = 0 if A(n)>=2 & A(n) is even; B(n) = 2 if A(n) >= 2 & A(n) is odd. Then A075325(n) = (5n+B(n)-4)/2. - John Chew (jjchew(AT)math.utoronto.ca), Jun 20 2006
|
|
EXAMPLE
|
The first pair (1, 3) covers 1, 2, 3. The second pair is (4, 9) covering 4, 5, 9.
|
|
PROGRAM
|
(PARI) used = vector(500); i = 1; A = vector(80); B = A; C = A; for (n = 1, 80, while (used[i], i++); j = i + 1; while (used[j] || used [i + j], j++); A[n] = i; B[n] = i + j; C[n] = i + i + j; used[i] = 1; used[j] = 1; used[i + j] = 1); A (Wasserman)
|
|
CROSSREFS
|
Cf. A075326, A075327.
The sequence formed by listing the differences between the second and first elements of each pair is A047215.
Sequence in context: A086377 A003662 A134779 this_sequence A026278 A139404 A014455
Adjacent sequences: A075322 A075323 A075324 this_sequence A075326 A075327 A075328
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 16 2002
|
|
EXTENSIONS
|
More terms from David Wasserman (dwasserm(AT)earthlink.net), Jan 16 2005
|
|
|
Search completed in 0.002 seconds
|
