|
%I #23 Nov 04 2018 20:33:26
%S 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,
%T 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,
%U 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
%N Break up the list of values of the Euler totient function phi(k) into nondecreasing runs; sequence gives lengths of successive runs.
%H Seiichi Manyama, <a href="/A303579/b303579.txt">Table of n, a(n) for n = 1..10000</a>
%e The initial values of d(k) = A000010(k) for k = 1,2,3,... are
%e 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, ...
%e Breaking this up into nondecreasing runs we get:
%e [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], ...
%e whose successive lengths are
%e 5, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
%o (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
%Y Cf. A000010.
%Y A303580(m) gives value of n that starts the m-th run.
%Y For run lengths in this sequence see A302441.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Apr 29 2018
%E More terms from _Seiichi Manyama_, Apr 29 2018
|
