A308248
Squares of automorphic numbers in base 6 (cf. A237583).
Original entry on oeis.org
0, 1, 9, 16, 81, 784, 6561, 18496, 1478656, 43046721, 281165824, 893352321, 5859137025, 41368305664, 405026597889, 1088266240000, 15965210931201, 36991307874304, 583272781383681, 1318789102698496
Offset: 1
784 = 3344_6 and sqrt(3344_6) = 44_6. Hence 784 is in the sequence.
A201821
Automorphic numbers: n^2 ends with n in base 6 (written in base 6).
Original entry on oeis.org
0, 1, 3, 4, 13, 44, 213, 344, 5344, 50213, 205344, 350213, 1350213, 4205344, 21350213, 34205344, 221350213, 334205344, 2221350213, 3334205344, 52221350213, 152221350213, 403334205344, 5152221350213, 55152221350213, 155152221350213, 400403334205344
Offset: 1
a(3) = (3)_6 = 3 since 3^2 = 9 = (13)_6 ends with 3 in base 6.
a(4) = (4)_6 = 4 since 4^2 = 16 = (24)_6 ends with 4 in base 6.
a(5) = (13)_6 = 9 since 9^2 = 81 = (213)_6 ends with 13 in base 6.
- Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 147.
- Maurice Kraitchik, Mathematical Recreations, New York, Dover, (2nd ed.) 1953, p. 77.
A201919
Automorphic numbers n^2 ends with n in base 14 (written in base 10).
Original entry on oeis.org
0, 1, 7, 8, 49, 148, 344, 2401, 36016, 151264, 386561, 1764736, 5764801, 46941952, 58471553, 374712065, 1101076992, 4802079233, 15858967552, 139825248256, 149429406721, 1595702681601, 2453862488064, 14602557997056, 42091354378241, 127990382747648
Offset: 1
a(3) = 7 = (7)_14 since 7^2 = 49 = (37)_14 ends with 7 in base 14.
a(4) = 8 = (8)_14 since 8^2 = 64 = (48)_14 ends with 8 in base 14.
a(5) = 49 = (37)_14 since 49^2 = 2401 = (C37)_14 ends with 37 in base 14.
A201918
Automorphic numbers: n^2 ends with n in base 12 (written in base 10).
Original entry on oeis.org
0, 1, 4, 9, 64, 81, 513, 1216, 6400, 14337, 234496, 483328, 2502657, 17432577, 18399232, 412549120, 842530816, 4317249537, 11162091520, 50755272705, 692253097984, 2178269839360, 6737830608897, 46758772080640, 60234433298433, 474731593596928, 809186870951937
Offset: 1
a(3) = 4 = (4)_12 since 4^2 = 16 = (14)_12 ends with 4 in base 12.
a(4) = 9 = (9)_12 since 9^2 = 81 = (69)_12 ends with 9 in base 12.
a(5) = 64 = (54)_12 since 64^2 = 4096 = (2454)_12 ends with 54 in base 12.
-
a201918[n_Integer] := Module[{i = 0}, Flatten[Last[Reap[
Do[If[
IntegerDigits[i^2, 12][[-Length[IntegerDigits[i, 12]] ;; -1]] ==
IntegerDigits[i, 12], Sow[i]], {i, n}]]]]]; a201918[12^6] (* Michael De Vlieger, Aug 13 2014 *)
-
# See A003226. - Eric M. Schmidt, Feb 09 2014
A201921
Automorphic numbers: n^2 ends with n in base 15 (written in base 10).
Original entry on oeis.org
0, 1, 6, 10, 100, 126, 1000, 2376, 4375, 46251, 156250, 603126, 3640626, 7750000, 19140625, 151718751, 835156251, 1727734375, 5960937501, 32482421875, 236621093751, 340029296875, 8413134765625, 60784912109376, 68961425781250, 709516601562501, 1236678466796875
Offset: 1
a(3) = 6 = (6)_15 since 6^2 = 36 = (26)_15 ends with 6 in base 15.
a(4) = 10 = (A)_15 since 10^2 = 100 = (6A)_15 ends with A in base 15.
a(5) = 100 = (6A)_15 since 100^2 = 10000 = (2E6A)_15 ends with 6A in base 15.
A201948
Automorphic numbers: n^2 ends with n in base 18 (written in base 10).
Original entry on oeis.org
0, 1, 9, 10, 81, 244, 729, 5104, 6561, 98416, 413344, 1476225, 9034497, 24977728, 263063296, 349156737, 2711943424, 8308017153, 96467701761, 101891588608, 1286623443969, 2283843782656, 30847581595648, 33420828483585, 352189631991808, 804641749434369
Offset: 1
a(3) = 9 = (9)_18 since 9^2 = 81 = (49)_18 ends with 9 in base 18.
a(4) = 10 = (A)_18 since 10^2 = 100 = (5A)_18 ends with A in base 18.
a(5) = 81 = (49)_18 since 81^2 = 6561 = (1249)_18 ends with 49 in base 18.
A259986
This sequence and A259987 are base-6 analogs of A007185 and A016090, written in base 10.
Original entry on oeis.org
3, 9, 81, 81, 6561, 29889, 76545, 636417, 3995649, 24151041, 326481921, 689278977, 11573190657, 76876660737, 155240824833, 2035980763137, 4857090670593, 55637069004801, 157197025673217, 1375916505694209, 19656708706009089, 129341461907898369
Offset: 1
- C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.
A259987
This sequence and A259986 are base 6 analogs of A007185 and A016090, written in base 10.
Original entry on oeis.org
4, 28, 136, 1216, 1216, 16768, 203392, 1043200, 6082048, 36315136, 36315136, 1487503360, 1487503360, 1487503360, 314944159744, 785129144320, 12069568774144, 45922887663616, 452162714337280, 2280241934368768, 2280241934368768, 2280241934368768, 2280241934368768
Offset: 1
- C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.
A259988
This sequence and A259989 are base-6 analogs of A007185 and A016090, written in base 6.
Original entry on oeis.org
3, 13, 213, 213, 50213, 350213, 1350213, 21350213, 221350213, 2221350213, 52221350213, 152221350213, 5152221350213, 55152221350213, 155152221350213, 4155152221350213, 14155152221350213, 314155152221350213, 1314155152221350213, 21314155152221350213
Offset: 1
- C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.
-
def a(n) : return Integer(crt(1, 0, 2^n, 3^n).str(6)) # Eric M. Schmidt, Jul 18 2015
A259989
This sequence and A259988 are base-6 analogs of A007185 and A016090, written in base 6.
Original entry on oeis.org
4, 44, 344, 5344, 5344, 205344, 4205344, 34205344, 334205344, 3334205344, 3334205344, 403334205344, 403334205344, 403334205344, 400403334205344, 1400403334205344, 41400403334205344, 241400403334205344, 4241400403334205344, 34241400403334205344
Offset: 1
- C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.
-
def a(n) : return Integer(crt(0, 1, 2^n, 3^n).str(6)) # Eric M. Schmidt, Jul 18 2015
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