A050727 Numbers k such that the decimal expansion of 6^k contains no pair of consecutive equal digits (probably finite).

0, 1, 2, 3, 4, 8, 11, 13, 14, 15, 26

Offset

1,3

Comments

No additional terms up to 25000. - Harvey P. Dale, Oct 17 2011

No additional terms up to 100000. - Michel Marcus, Oct 16 2019

No additional terms up to 10^7. - Lucas A. Brown, Mar 02 2024

Links

Table of n, a(n) for n=1..11.

Example

6^26 = 170581728179578208256 where no consecutive digits are equal.

Mathematica

Select[Range[120], !MemberQ[Differences[IntegerDigits[6^#]], 0]&] (* Harvey P. Dale, Oct 17 2011 *)

Prog

(PARI) isok(n) = {my(d = digits(6^n), c = d[1]); for (i=2, #d, if (d[i] == c, return (0)); c = d[i]; ); return (1); } \\ Michel Marcus, Oct 16 2019
(Python)
try: from gmpy2 import mpz; x = mpz(1)
except: x = 1
print(0)
k = 1
while True:
    print('\b'*42 + str(k), end='')
    x *= 6  # x == 6**k
    y, flag = x, True
    y, a = divmod(y, 10)
    while y > 6:
        b = a
        y, a = divmod(y, 10)
        if a == b:
            flag = False
            break
    if flag: print()
    k += 1
# Lucas A. Brown, Mar 02 2024

Crossrefs

Cf. A000400, A030702, A046264, A046272.

Sequence in context: A106131 A275646 A279194 * A295323 A102951 A015935

Adjacent sequences: A050724 A050725 A050726 * A050728 A050729 A050730

Keyword

nonn,base,more

Author

Patrick De Geest, Sep 15 1999

Status

approved