OFFSET
1,3
COMMENTS
This sequence is infinite as it contains 5 * A094028(k) for any k > 0.
Also contains terms with patterns 2(46802)^k, 4(82604)^k, 6(28406)^k, 8(64208)^k, 1(2345678901)^k, 3(6925814703)^k, 7(4185296307)^k, 9(8765432109)^k for k >= 0, where ^ denotes repeated concatenation; all terms have first and last digits the same. - Michael S. Branicky, May 29 2021
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..426
Rémy Sigrist, PARI program for A344822
EXAMPLE
- 4 * 1 = 4 mod 10,
- 4 * 2 = 8 mod 10,
- 4 * 3 = 2 mod 10,
- 4 * 4 = 6 mod 10,
- 4 * 5 = 0 mod 10,
- 4 * 6 = 4 mod 10,
so 482604 is a term.
PROG
(PARI) is(n) = { my (d=digits(n)); for (k=1, #d, if (d[k] != (n*k)%10, return (0))); return (1) }
(PARI) See Links section.
(Python)
def ok(m):
d = str(m)
return all(d[i-1] == str((m*i)%10) for i in range(1, len(d)+1))
print(list(filter(ok, range(10**6)))) # Michael S. Branicky, May 29 2021
(Python)
def auptod(maxdigits):
alst = [0]
for k in range(1, maxdigits+1):
for d1 in range(1, 10):
d = [(d1*i)%10 for i in range(1, k+1)]
if d1 == d[-1]: alst.append(int("".join(map(str, d))))
return alst
print(auptod(16)) # Michael S. Branicky, May 29 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 29 2021
STATUS
approved