A050732
Numbers of form 2^k (for values of k see A050723) containing no pair of consecutive equal digits (probably finite).
Original entry on oeis.org
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 131072, 1048576, 2097152, 4194304, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 17179869184, 34359738368, 68719476736, 137438953472
Offset: 1
2^18 = 262144 is missing, for example.
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Select[2^Range[0,40],FreeQ[Differences[IntegerDigits[#]],0] &] (* Jayanta Basu, May 31 2013 *)
A052057
Numbers k such that the decimal expansion of 2^k contains no palindromic substring except single digits.
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 29, 37, 54
Offset: 1
Record number is 2^54 = 18014398509481984.
A050725
Decimal expansion of 4^n contains no pair of consecutive equal digits (probably finite).
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 14, 15, 16, 17, 18, 24, 27, 28, 33, 34, 40, 52, 63
Offset: 1
4^63 = 85070591730234615865843651857942052864.
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Select[Range[0,70],FreeQ[Differences[IntegerDigits[4^#]],0]&] (* Harvey P. Dale, Jul 25 2013 *)
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isok(n) = {my(d = digits(4^n), c = d[1]); for (i=2, #d, if (d[i] == c, return (0)); c = d[i];); return (1);} \\ Michel Marcus, Oct 16 2019
A171550
Numbers n with property that decimal expansion of 2^n+3^n contains no pair of neighbor equal digits (probably finite).
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 22, 23, 26, 27, 29, 45, 52, 73
Offset: 0
2^73+3^73 = 67585198634826967968486182914745315.
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Reap[Do[id=IntegerDigits[2^m+3^m];rm=Rest[id]-Most[id];If[FreeQ[rm,0],Sow[m]],{m,0,10000}]][[2,1]]
Select[Range[0,80],FreeQ[Differences[IntegerDigits[2^#+3^#]],0]&] (* Harvey P. Dale, Dec 09 2021 *)
A171551
Numbers n with property that decimal expansion of 3^n-2^n contains no pair of neighbor equal digits (probably finite).
Original entry on oeis.org
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
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).
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Reap[Do[id=IntegerDigits[3^m-2^m];rm=Rest[id]-Most[id];If[FreeQ[rm,0],Sow[m]],{m,0,10000}]][[2,1]]
Showing 1-5 of 5 results.
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