A367740 a(n) = A367727(A367593(n)).

-1, 0, 0, 0, 5, 0, 9, 5, 0, 5, 0, 5, 0, 5, 3, 0, 5, 0, 8, 5, 0, 8, 5, 0, 8, 5, 3, 0, 8, 5, 0, 8, 5, 3, 0, 8, 5, 0, 8, 5, 3, 0, 8, 5

Offset

1,5

Comments

Restricted to integers k where k + 1 divides R(k) - 1 the terms are (R(k) - 1) / (k + 1), where R(k) denotes the digit reversal of k. - Peter Luschny, Dec 01 2023

The 0's correspond to the powers of 10 (cf. A011557), the 5's correspond to the numbers of the form 14*10^h + 7 = 7*A199682(h) for h > 0, and the 8's correspond to the numbers of the form 12345*10^m + 6789 = A367650(m) for m > 3. The only negative term -1 corresponds to A367593(1) = 0. - Stefano Spezia, Dec 01 2023

Links

Table of n, a(n) for n=1..44.

Formula

-1 <= a(n) <= 9.

Prog

(Python)
def A367740List(upto):
    L = []
    for n in range(upto):
        rev = int(str(n)[::-1])
        if (rev - 1) % (n + 1) == 0:
            L.append((rev - 1) // (n + 1))
    return L
print(A367740List(10**6))  # Peter Luschny, Dec 01 2023
(Python)
from itertools import product, count, islice
def A367740_gen(): # generator of terms
    yield from (-1, 0, 0)
    for l in count(1):
        m = 10**(l+1)
        for d in product('0123456789', repeat=l):
            for a, b, c in ((1, 0, 0), (1, 1, 0), (1, 4, 2), (1, 5, 5), (1, 7, 5)):
                k = a*m+int(s:=''.join(d))*10+b
                r = b*m+int(s[::-1])*10+a
                if c*(k+1)==r-1:
                    yield c
            a, b = 1, 9
            k = a*m+int(s:=''.join(d))*10+b
            r = b*m+int(s[::-1])*10+a
            p, q = divmod(r-1, k+1)
            if not q:
                yield p
        a, b, c=2, 6, 3
        for d in product('0123456789', repeat=l):
            k = a*m+int(s:=''.join(d))*10+b
            r = b*m+int(s[::-1])*10+a
            if c*(k+1)==r-1:
                yield c
A367740_list = list(islice(A367740_gen(), 20)) # Chai Wah Wu, Dec 01 2023

Crossrefs

Cf. A367593, A367727, A367728.

Cf. A004086, A011557, A199682, A367650.

Sequence in context: A199184 A159692 A271175 * A196769 A019925 A101115

Adjacent sequences: A367737 A367738 A367739 * A367741 A367742 A367743

Keyword

sign,base,hard,more

Author

Stefano Spezia, Nov 29 2023

Extensions

a(30)-a(44) from Chai Wah Wu, Dec 02 2023

Status

approved