A303579 Break up the list of values of the Euler totient function phi(k) into nondecreasing runs; sequence gives lengths of successive runs.

5, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Example

The initial values of d(k) = A000010(k) for k = 1,2,3,... are
1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, ...
Breaking this up into nondecreasing runs we get:
[1, 1, 2, 2, 4], [2, 6], [4, 6], [4, 10], [4, 12], [6, 8, 8, 16], [6, 18], [8, 12], [10, 22], [8, 20], [12, 18], [12, 28], [8, 30], [16, 20], [16, 24], [12, 36], [18, 24], [16, 40], [12, 42], [20, 24], [22, 46], [16, 42], [20, 32], [24, 52], [18, 40], [24, 36], [28, 58], [16, 60], [30, 36], [32, 48], [20, 66], [32, 44], [24, 70], [24, 72], [36, 40], ...
whose successive lengths are
5, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...

Prog

(PARI) upto(n) = {my(res = List(), t = 1, l = 1); for(i = 2, n, el = eulerphi(i); if(el >= l, t++, listput(res, t); t = 1); l = el); res} \\ David A. Corneth, Apr 29 2018

Crossrefs

Cf. A000010.

A303580(m) gives value of n that starts the m-th run.

For run lengths in this sequence see A302441.

Sequence in context: A190288 A325499 A081119 * A306966 A286016 A119320

Adjacent sequences: A303576 A303577 A303578 * A303580 A303581 A303582

Keyword

nonn

Author

N. J. A. Sloane, Apr 29 2018

Extensions

More terms from Seiichi Manyama, Apr 29 2018

Status

approved