OFFSET
1,1
COMMENTS
a(1) = 1, a(n+1) = a(n) + phi(a(n)) gives A074693.
For n > 1, a(n)/3 is 2^(2^(n-2)). This sequence is 2, 4, 16, 256, ..., which is phi(a(n-1)).
The Harris 1935 problem is to show 1 + sqrt(13) = sqrt(12 + sqrt(48 + sqrt( 768 + ...))). - Michael Somos, Jun 18 2018
LINKS
V. C. Harris, Problem 78, National Mathematics Magazine 9, no.6 (1935), p. 180.
Dixon Jones, A chronology of continued square roots and other continued compositions, through the year 2016, arXiv:1707.06139, 2018. See bibliography item 80.
FORMULA
a(n) = 3*2^(2^(n-2)).
EXAMPLE
a(3) = 12 and phi(12)= 4, hence a(4) = 12*4 = 48.
MATHEMATICA
RecurrenceTable[{a[1]==3, a[n+1]==a[n] EulerPhi [a[n]]}, a, {n, 20}] (* Vincenzo Librandi, Jun 19 2018 *)
NestList[# EulerPhi[#]&, 3, 10] (* Harvey P. Dale, Jun 23 2022 *)
PROG
(PARI) for(n=1, 11, if(n==1, a=3, a*=eulerphi(a)); print1(a, ", "); )
(Magma) [3] cat [3*2^(2^(n-2)): n in [2..11]]; // Vincenzo Librandi, Jun 19 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Jul 06 2003
EXTENSIONS
More terms from Ray Chandler, Jul 16 2003
STATUS
approved