|
Search: id:A105210
|
|
|
| A105210 |
|
a(1) = 393; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1). |
|
+0
6
|
|
| 393, 528, 545, 660, 682, 727, 728, 751, 752, 802, 1206, 1279, 1280, 1288, 1321, 1322, 1986, 2323, 2448, 2471, 2832, 2897, 2898, 2934, 3103, 3240, 3251, 3252, 3529, 3530, 3891, 5192, 5265, 5287, 5616, 5635, 5671, 5832, 5838, 5990, 6597, 7334, 7549, 7550
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
In Math. Mag. 48 (1975) 301 one finds "C. W. Trigg, C. C. Oursler and R. Cormier and J. L. Selfridge have sent calculations on Problem 886 [Nov 1973] for which we had received only partial results [Jan 1975]. Cormier and Selfridge sent the following results: There appear to be five sequences beginning with integers less than 1000 which do not merge. These sequences were carried out to 10^8 or more." The five sequences are A003508, A105210-A105213.
This suggests that there may be infinitely many different (non-merging) sequences obtained by choosing different starting values.
|
|
REFERENCES
|
Problem 886, Math. Mag., 48 (1975), 57-58.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..2000
|
|
EXAMPLE
|
a(2)=528 because a(1)=393, the distinct prime factors of a(1) are 3 and 131; finally, 1+393+3+131=528.
|
|
MAPLE
|
with(numtheory): p:=proc(n) local nn, ct, s: if isprime(n)=true then s:=0 else nn:=convert(factorset(n), list): ct:=nops(nn): s:=sum(nn[j], j=1..ct):fi: end: a[1]:=393: for n from 2 to 50 do a[n]:=1+a[n-1]+p(a[n-1]) od:seq(a[n], n=1..50); (Deutsch)
|
|
MATHEMATICA
|
a[1] = 393; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 44}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2005)
a[1] = 412; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 43}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2005)
a[1] = 668; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2005)
a[1] = 932; a[n_] := a[n] = a[n - 1] + 1 + Plus @@ Select[ Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[a[n - 1]]], # < a[n - 1] &]; Table[a[n], {n, 40}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2005)
|
|
CROSSREFS
|
Sequence in context: A105233 A048129 A045194 this_sequence A158002 A083752 A047825
Adjacent sequences: A105207 A105208 A105209 this_sequence A105211 A105212 A105213
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
R. K. Guy, Apr 14, 2005
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 14 2005
|
|
|
Search completed in 0.005 seconds
|
