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A067579
Conjectured values of a(n) defined by: a(n) = first prime appearing in the orbit n, f(n), f(f(n)),...., if it exists; = 0 otherwise, where f(n) = n + sigma(n).
0
2, 2, 3, 11, 5, 137, 7, 23, 0, 0, 11, 0, 13, 269, 479, 47, 17, 137, 19, 61223, 53, 0, 23, 0, 0, 0, 67, 0, 29, 0, 31, 479, 0, 0, 83, 127, 37, 269, 479, 0
OFFSET
1,1
COMMENTS
The values n with a(n) = 0 listed here are conjectural. There is no prime < 10^30 appearing in the orbits of these values.
EXAMPLE
The orbit of 4 is 4, 11, 23,.... and the first prime in the orbit is 11. So a(4) = 11.
MATHEMATICA
f[ n_ ] := n + DivisorSigma[ 1, n ]; h[ n_ ] := Module[ { a = n}, While[ ! PrimeQ[ a ] && a < 10^30, a = f[ a ] ]; If [ ! PrimeQ[ a ], a = 0 ]; a ]; Table[ h[ i ], {i, 1, 40} ]
CROSSREFS
Sequence in context: A153920 A300483 A294241 * A019143 A084650 A067919
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Jan 30 2002
STATUS
approved