A174965 Length of the n-th run of consecutive terms in A000961.

5, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Pahikkala Jussi, Apr 02 2010

Keywords

• nonn

Comments

Let b(n) be partial sums of this sequence, as b(0) = 0, b(n) = b(n-1) + a(n). Then 2's in this sequence occur at certain positions k so that A000961(b(k))-1 = one of the terms of A006549. E.g., a(6625) = 2, and b(6625) = 6637, with A000961(6637) = 65537, the end of 2-run (65536,65537) in A000961. (The start of that 2-run, 65536, is listed as A006549(12), and 12 = 6637-6625.) - Antti Karttunen, Jul 24 2017

Position of 2s: {5, 11, 36, 62, 1068, 6625, 12358, 43566, ...},

position of 3: {2}, position of 5: {1}. All other positions pertain to 1 for A000961(n) <= 10^8. - Michael De Vlieger, Jul 25 2017

Examples

			n a(n) run in A000961
1:  5 (1 2 3 4 5)
2:  3 (7 8 9)
3:  1 (11)
4:  1 (13)
5:  2 (16 17)
6:  1 (19)
7:  1 (23)
8:  1 (25)
9:  1 (27)
10: 1 (29)
11: 2 (31 32)
12: 1 (37)
13: 1 (41)
14: 1 (43)
15: 1 (47)
16: 1 (49)
17: 1 (53)
18: 1 (59)
19: 1 (61)
20: 1 (64)
21: 1 (67)
22: 1 (71)
23: 1 (73)
24: 1 (79)
25: 1 (81)
26: 1 (83)
27: 1 (89)
28: 1 (97)
29: 1 (101)
30: 1 (103)
31: 1 (107)
32: 1 (109)
33: 1 (113)
34: 1 (121)
35: 1 (125)
36: 2 (127 128)
37: 1 (131)
38: 1 (137)
etc.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..9987 (computed by using the 10000 term b-file of A000961 computed by T. D. Noe)

Crossrefs

Cf. A000961, A006549, A057820.

Programs

Mathematica

With[{n = 500}, Function[s, Function[t, Length /@ DeleteCases[Split@ ReplacePart[t, Map[# -> 1 &, s]], k_ /; First@ k == 0]]@ ConstantArray[0, Max@ s]]@ Sort@ Flatten[{{1}}~Join~Array[Function[p, Map[p^# &, Range@ Floor@ Log[p, n]] ][Prime@ #] &, PrimePi@ n]]] (* Michael De Vlieger, Jul 25 2017 *)

Extensions

Terms a(33) & a(36) corrected, more terms added by Antti Karttunen, Jul 24 2017