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A171551
Numbers k such that the decimal expansion of 3^k - 2^k contains no pair of consecutive equal digits (probably finite).
1
0, 1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 15, 18, 20, 21, 22, 23, 24, 26, 27, 29, 37, 50
OFFSET
0,3
EXAMPLE
50 is a term because 3^50-2^50 = 717897986565952681927625,
while 49 is not because 3^49-2^49 = 2392(99)328(66)7(66)7576168(77)1 (four pairs of neighbor equal digits).
MAPLE
filter:= proc(k) local L;
L:= convert(3^k-2^k, base, 10);
not has(L[2..-1]-L[1..-2], 0)
end proc:
select(filter, [$0..1000]); # Robert Israel, Oct 03 2025
MATHEMATICA
Reap[Do[id=IntegerDigits[3^m-2^m]; rm=Rest[id]-Most[id]; If[FreeQ[rm, 0], Sow[m]], {m, 0, 10000}]][[2, 1]]
CROSSREFS
Cf. A001047, A050723 (2^n), A050724 (3^n), A171550 (3^n+2^n).
Sequence in context: A121405 A330217 A231003 * A096199 A104576 A332485
KEYWORD
nonn,base,more
AUTHOR
Zak Seidov, Dec 11 2009
STATUS
approved