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

Author

Stefano Spezia, Nov 29 2023

Keywords

• sign
• base
• hard
• more

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

Crossrefs

Cf. A367593, A367727, A367728.

Cf. A004086, A011557, A199682, A367650.

Programs

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

Formula

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

Extensions

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