A342388 Integers y corresponding to the terms of A342387.

6, 55, 474, 9360, 80029, 355452, 684228, 512562258, 986657022, 4382255359, 37466984190, 739114421304, 6319209189385, 54027365220036, 9112295268838531, 40472427468293976, 77907423180308442, 346027256676968725, 58361212342395772530, 498971064164650006699, 4266054677084570952198

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

Cf. A342387.

Sequence in context: A295548 A198855 A318592 * A253475 A215853 A110431

Adjacent sequences: A342385 A342386 A342387 * A342389 A342390 A342391

Keyword

nonn,base

Author

Michel Marcus, Mar 10 2021

Extensions

More terms from Chai Wah Wu, Mar 10 2021

Status

approved