A161772 -id:A161772 - cp's OEIS frontend

A161773 The number of pattern sequences if the "sum the cubes of the digits" pattern is applied in bases 2 through 10.

1, 3, 9, 4, 5, 15, 7, 12, 9

Offset: 2

Brian Gleason (gleason(AT)uga.edu), Jun 18 2009

			Base 2 has one such pattern: 1, 1, 1, 1, 1, ...
Base 3 has 3 such patterns, etc...

Brian Gleason, Some (Probably Useless) Number Theory

A161772

A250202 The "sum of squares of digits" problem in base 12, start with 6 (written in base 10).

Original entry on oeis.org

6, 36, 9, 81, 117, 162, 38, 13, 2, 4, 16, 17, 26, 8, 64, 41, 34, 104, 128, 164, 66, 61, 26, 8, 64, 41, 34, 104, 128, 164, 66, 61, 26, 8, 64, 41, 34, 104, 128, 164, 66, 61, 26, 8, 64, 41, 34, 104, 128, 164, 66, 61, 26, 8, 64, 41, 34, 104, 128, 164, 66, 61, 26, 8, 64, 41

Offset: 1

Eric Chen, Mar 13 2015

Periodic with period 10.
In base 12, there are 3 fixed points and 4 cycles (only 1 fixed point and 1 cycle in base 10, see A161772):
1 -> 1 (length 1);
5 -> 21 -> 5 (length 2);
8 -> 54 -> 35 -> 2a -> 88 -> a8 -> 118 -> 56 -> 51 -> 22 -> 8 (length 10);
18 -> 55 -> 42 -> 18 (length 3);
25 -> 25 (length 1);
68 -> 84 -> 68 (length 2);
a5 -> a5 (length 1);
Notice 25 (decimal 29) and a5 (decimal 125) are Armstrong numbers in base 12 (A161949), there are no 2-digit Armstrong numbers in base 10.
In base 12, there are only few happy numbers (no such between 10 (decimal 12) and 100 (decimal 144)), but in base 10, there are 20 happy numbers less than or equal to 100 (see A007770).

Eric Chen, Table of n, a(n) for n = 1..1000
Eric Chen, List of A250202 starts with n for n up to 40 (decimal 48)
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A000216, A000218, A080709, A000221, A008460, A008461, A008462, A008463, A161772.

NestList[Total[IntegerDigits[#, 12]^2]&, 6, 144]
Join[{6, 36, 9, 81, 117, 162, 38, 13, 2, 4, 16, 17},LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{26, 8, 64, 41, 34, 104, 128, 164, 66, 61},54]] (* Ray Chandler, Aug 26 2015 *)
PadRight[{6,36,9,81,117,162,38,13,2,4,16,17},80,{66,61,26,8,64,41,34,104,128,164}] (* Harvey P. Dale, Aug 06 2017 *)

a(n) = [6, 36, 9, 81, 117, 162, 38, 13, 2, 4, 16, 17, 26, 8, 64, 41, 34, 104, 128, 164, 66, 61][n%10+10*(n>=10)+10*(n%10<3 & n>=20)]

A161775 The number of pattern sequences if the "sum the fourth powers of the digits" pattern is applied in bases 2 through 10.

Original entry on oeis.org

1, 3, 4, 7, 4, 6, 7, 5, 6

Offset: 2

Brian Gleason (gleason(AT)uga.edu), Jun 18 2009

			Base 2 has one such pattern: 1, 1, 1, 1, 1, ...
Base 3 has 3 such patterns, etc...

Brian Gleason, Some (Probably Useless) Number Theory

A161773 A161772

cp's OEIS Frontend

A161773 The number of pattern sequences if the "sum the cubes of the digits" pattern is applied in bases 2 through 10.

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A250202 The "sum of squares of digits" problem in base 12, start with 6 (written in base 10).

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A161775 The number of pattern sequences if the "sum the fourth powers of the digits" pattern is applied in bases 2 through 10.

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