|
Search: id:A130798
|
|
|
| A130798 |
|
a(1)=1. a(n+1) = a(n) + (number of terms, from among the first n terms of the sequence, which occur among (d(1),d(2),d(3),...d(n)), where d(n) = A000005(n)). |
|
+0
2
|
|
| 1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The first differences never decrease so a very concise sequence from which this sequence can be reconstituted is the number of terms whose first difference is k: 1, 4, 6, 12, 24, 72, 720, 120, 300, 36, 384, 840, 552, 1024, 944, 1680, 840, 2520, ..., - Robert G. Wilson v.
|
|
EXAMPLE
|
The terms among the first 12 terms of {a(k)} which occur among the first 12 values of sequence A000005 are a(1) = 1 (A000005(1)), a(2) = 2 (A000005(2)), a(3) = 4 (A000005(6)), and a(4) = 6 (A000005(12)). There are 4 such terms, so a(13) = a(12) + 4 = 32.
|
|
MAPLE
|
with(numtheory): a[1] := 1: for n from 2 to 60 do a[n] := a[n-1]+nops(`intersect`({seq(a[i], i = 1 .. n-1)}, {seq(tau(i), i = 1 .. n-1)})) end do: seq(a[n], n = 1 .. 60); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 21 2007
|
|
MATHEMATICA
|
f[l_] := Append[l, l[[ -1]] + Count[MemberQ[l, # ] & /@ Union@ DivisorSigma[0, Range@ Length@ l], True]]; Nest[f, {1}, 59] (* Robert G. Wilson v (rgwv@rgwv.com), Aug 26 2007 *)
|
|
CROSSREFS
|
Cf. A000005. See A105434 for a variant.
Sequence in context: A129011 A130174 A061168 this_sequence A025224 A096182 A056827
Adjacent sequences: A130795 A130796 A130797 this_sequence A130799 A130800 A130801
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Leroy Quet (qq-quet(AT)mindspring.com), Jul 15 2007
|
|
EXTENSIONS
|
More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 18 2007
|
|
|
Search completed in 0.002 seconds
|
