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A121229
Beginning with a(1) = 1 and a(2) = 2, a(n) is not equal to the product of two consecutive (distinct) earlier terms.
6
1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78
OFFSET
1,2
LINKS
MAPLE
A121229 := proc(n)
option remember;
local a, ispr, i;
if n <=2 then
n;
else
for a from procname(n-1)+1 do
ispr := false ;
for i from 1 to n-2 do
if procname(i)*procname(i+1) = a then
ispr := true ;
break;
end if;
end do:
if not ispr then
return a;
end if;
end do:
end if;
end proc: # R. J. Mathar, May 25 2017
MATHEMATICA
a[n_] := a[n] = Module[{k, ispr, i}, If[n <= 2, n, For[k = a[n - 1] + 1, True, k++, ispr = False; For[i = 1, i <= n - 2, i++, If[a[i]*a[i + 1] == k, ispr = True; Break[]]]; If[!ispr, Return[k]]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 23 2022, after R. J. Mathar *)
PROG
(Python)
from itertools import islice
def agen(): # generator of terms
disallowed, prevk, k = {1, 2}, 2, 3; yield from [1, 2]
while True:
while k in disallowed: k += 1
yield k; disallowed.update([k, k*prevk]); prevk = k
print(list(islice(agen(), 72))) # Michael S. Branicky, Sep 23 2022
CROSSREFS
The complement is A286290, excluding the initial 1.
Sequence in context: A303234 A175233 A346130 * A286291 A286926 A145198
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Aug 21 2006
STATUS
approved