A060611
Smallest prime p such that n = A049108(p) = length of chain of iterates of Euler Phi starting with p.
Original entry on oeis.org
2, 3, 5, 11, 17, 41, 83, 137, 257, 641, 1097, 2657, 5441, 10883, 17477, 40961, 65537, 140417, 295937, 557057, 1193537, 2384897, 4227137, 9548417, 17966357, 35946497, 71304257, 162174977, 305268737, 541073537, 1212153857, 2281701377
Offset: 2
n=13: a(13)=2657 is the smallest prime which gives a chain of length 13, 2657 -> 2656 -> 1312 -> 640 -> 256 -> 128 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1, while the smallest number having this property is A007755(13) = 2329 -> 2176 -> 1024 -> 512 -> 256 -> 128 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1.
A007755 has the same initial terms but is a different sequence.
Removed duplicate cross references, added link, reformulated example. -
M. F. Hasler, Oct 25 2008
A227946
Smallest m such that the number of iterations of "take odd part of phi" to reach 1 from m (A227944) is n.
Original entry on oeis.org
1, 2, 7, 19, 47, 163, 487, 1307, 2879, 19683, 39367, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 86093443, 258280327, 688747547, 3486784401, 10460353203
Offset: 0
a(1) = 2 because just one step is needed to reach 1 from 2, since phi(2) = 1. The numbers 3, 4, 5 and 6 also take one step.
a(2) = 7 because two steps are needed to reach 1 from 7: phi(7) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1. The numbers from 8 to 18 take one or two steps to reach 1.
a(3) = 19 because three steps are needed to reach 1 from 19: phi(19) = 18, the odd part of which is 9, and phi(9) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.
A053476
Smallest number m such that when A051953 is applied n times to m the result is neither a power of 2 nor 0.
Original entry on oeis.org
9, 21, 42, 82, 130, 330, 450, 666, 1050, 1470, 1950, 2922, 4074, 5586, 7770, 11154, 15810, 22638, 30702, 42570, 53130, 68970, 107690, 159390, 206910, 289830, 395190, 610350, 823290, 1185570, 1522290, 2168250, 3011850, 4103490, 5364450
Offset: 1
a(6)=330 and the iteration of A051953 applied to 330 gives sequence {330,250,150,110,70,46,24,16,8,4,2,1,0}. Six iterations result in the 6th term 24 which still is neither a power of 2 nor 0. For smaller numbers than 330 these 6 iterations yield a power of 2 or the fixed number 0.
Cf.
A051953, see also its iterates.
Showing 1-3 of 3 results.
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