A237583
Automorphic numbers: n^2 ends with n in base 6.
Original entry on oeis.org
0, 1, 3, 4, 9, 28, 81, 136, 1216, 6561, 16768, 29889, 76545, 203392, 636417, 1043200, 3995649, 6082048, 24151041, 36315136, 326481921, 689278977, 1487503360, 11573190657, 76876660737, 155240824833, 314944159744, 785129144320, 2035980763137, 4857090670593
Offset: 1
From A201821:
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.
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
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.
Showing 1-5 of 5 results.