OFFSET
1,1
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..950
Josep M. Brunat and Joan-Carles Lario, A problem on concatenated integers, arXiv:2103.05306 [math.NT], 2021.
EXAMPLE
y=6 is a term with x=20 because 7/21 = 207/621.
PROG
(PARI) isok(x) = {for (y=1, x-1, if ((y+1)/(x+1) == eval(Str(x, y+1))/eval(Str(y, x+1)), return (y)); ); } \\ A342387
for (x=1, 10000, if (y=isok(x), print1(y, ", ")))
(Python)
A342388_list, x, s1, s2, m = [], 1, '1', '2', 10
while x < 10**6:
for y in range(1, x):
if (x+1)*int(s1+str(y+1)) == (y+1)*(y*m+x+1):
A342388_list.append(y)
break
x += 1
s1, s2 = s2, str(x+1)
m = 10**(len(s2)) # Chai Wah Wu, Mar 10 2021
(Python)
# based on formula in Brunat and Lario 2021
xlist, ylist, A342388_list, x, y = [4, 20, 39], [1, 6, 12], [6], 39, 12
while len(A342388_list) < 100:
if len(str(x+1)) == len(str(y+1))+1:
A342388_list.append(y)
x, y = 19*xlist[-3]+60*ylist[-3]+39, 6*xlist[-3]+19*ylist[-3]+12
xlist, ylist = xlist[1:] + [x], ylist[1:] + [y] # Chai Wah Wu, Mar 10 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Mar 10 2021
EXTENSIONS
More terms from Chai Wah Wu, Mar 10 2021
STATUS
approved