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A116300
n times n+9 gives the concatenation of two numbers m and m+1.
5
26, 66, 3416102887775247376839416334668635, 3756559953325598880263233435801764, 4313503800489302411917772257282208
OFFSET
1,1
LINKS
EXAMPLE
66 * 75 = 49//50, where // denotes concatenation.
MAPLE
F:= proc(d) local t, g, Cands:
t:= 10^d+1;
if NumberTheory:-QuadraticResidue(85, t) <> 1 then return NULL fi;
Cands:= map(s -> rhs(op(s)), [msolve(x^2 + 9*x - 1, t)]);
g:= proc(r) local v; v:= r^2 + 9*r - 1; v >= t*(t-11)/10 and v < t*(t-2) end proc;
op(sort(select(g, Cands)));
end proc:
map
map(F, [$1..82]); # Robert Israel, Aug 25 2023
PROG
(Python)
from itertools import count, islice
from sympy import sqrt_mod_iter
def A116300_gen(): # generator of terms
for l in count(1):
m = 10**l+1
k, r, dlist = m*(m-11)/10, m*(m-2), []
for a in sqrt_mod_iter(85, m):
d = ((a if a&1 else a+m)>>1)-4
if k<d*(d+9)<=r:
dlist.append(d)
yield from sorted(dlist)
A116300_list = list(islice(A116300_gen(), 14)) # Chai Wah Wu, May 07 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Giovanni Resta, Feb 06 2006
STATUS
approved