OFFSET
1,2
COMMENTS
If a prospective term is at least k(k-1) for a fixed value k, then the criterion will be satisfied for all d less than or equal to k.
Note that a(n) >= n, otherwise quotient for n would be 0 and so condition on remainder would not be satisfied. - Michel Marcus, Sep 04 2013
EXAMPLE
a(7)=21 because division by d=1 to 7 gives 21 r0, 10 r1, 7 r0, 5 r1, 4 r1, 3 r3 and 3 r0, respectively.
MAPLE
A134170 := proc(n)
local a, wrks, d;
for a from 1 do
wrks := true;
for d from 1 to n do
if modp(a, d) > floor(a/d) then
wrks := false;
break;
end if;
end do:
if wrks then
return a;
end if;
end do:
end proc: # R. J. Mathar, Sep 04 2013
PROG
(PARI) isok(m, n) = {for (d = 1, n, if (m\d < m%d, return (0)); ); return (1); }
a(n) = {m = 1; while (! isok(m, n), m++); m; } \\ Michel Marcus, Sep 03 2013
(Sage)
def FindM(n):
m=n-1
test=False
while not test:
test=True
m+=1
for d in [1..n]:
if Integer((m//d))<m.mod(d):
test=False
return m
[FindM(k) for k in [1..50]] # Tom Edgar, Sep 03 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Bryce Herdt (mathidentity(AT)yahoo.com), Jan 12 2008
EXTENSIONS
More terms added and incorrect conjecture removed by Michel Marcus, Sep 03 2013
STATUS
approved