cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A308250 Squares of automorphic numbers in base 12 (cf. A201919).

Original entry on oeis.org

0, 1, 49, 64, 2401, 21904, 118336, 5764801, 1297152256, 22880797696, 149429406721, 3114293149696, 33232930569601, 2203546857570304, 3418922510231809
Offset: 1

Views

Author

Jeremias M. Gomes, May 17 2019

Keywords

Examples

			2401 = c37_14 and sqrt(c37_14) = 37_14. Hence 2401 is in the sequence.

Crossrefs

Cf. A201919, A237583, A308250.

Programs

  • Sage
    [(n * n) for n in (0..1000000) if (n * n).str(base = 14).endswith(n.str(base = 14))]

Formula

Equals A201919(n)^2.

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

Views

Author

Eric M. Schmidt, Feb 09 2014

Keywords

Examples

			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.

Links

Crossrefs

Cf. A201821 (written in base 6), A003226, A201918, A201919, A201921, A201948.

Programs

  • PARI
    isok(n) = ((n^2-n) % 6^(#digits(n, 6))) == 0; \\ Michel Marcus, Mar 08 2014
  • Sage
    # See A003226.

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

Views

Author

Martin Renner, Dec 06 2011

Keywords

Examples

			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.

References

  • 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.

Crossrefs

Cf. A237583 (written in base 10), A003226, A201918, A201919, A201921, A201948.

Extensions

More terms from Eric M. Schmidt, Feb 09 2014

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

Views

Author

Martin Renner, Dec 06 2011

Keywords

Examples

			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.

Links

Crossrefs

Cf. A003226, A201821, A201919, A201921, A201948, A237583.

Programs

  • Mathematica
    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 *)
  • Sage
    # See A003226. - Eric M. Schmidt, Feb 09 2014

Extensions

More terms from 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

Views

Author

Martin Renner, Dec 06 2011

Keywords

Examples

			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.

Links

Crossrefs

Cf. A003226, A201821, A201918, A201919, A201948, A237583.

Programs

Extensions

More terms from 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

Views

Author

Martin Renner, Dec 06 2011

Keywords

Examples

			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.

Links

Crossrefs

Cf. A003226, A201821, A201918, A201919, A201921, A237583.

Programs

Extensions

More terms from Eric M. Schmidt, Feb 09 2014

A259991 This sequence and A259990 are base-14 analogs of A007185 and A016090, written in base 10.

Original entry on oeis.org

8, 148, 344, 36016, 151264, 1764736, 46941952, 1101076992, 15858967552, 139825248256, 2453862488064, 14602557997056, 127990382747648, 921705156001792, 56481739283791872, 523186025957228544, 15768859390622826496, 198716939766610001920, 3186868919241067200512
Offset: 1

Views

Author

N. J. A. Sloane, Jul 13 2015

Keywords

Comments

See Schut (1991) for precise definition.
Ignoring repetitions, the subsequence of A201919 of terms ending in 8 in base 14. - Eric M. Schmidt, Jul 18 2015

References

  • C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.

Links

Crossrefs

Cf. A007185, A016090, A201919, A259986-A259991.

Programs

  • Sage
    def a(n) : return crt(0, 1, 2^n, 7^n) # Eric M. Schmidt, Jul 18 2015

Extensions

More terms from Eric M. Schmidt, Jul 18 2015

A259990 This sequence and A259991 are base-14 analogs of A007185 and A016090, written in base 10.

Original entry on oeis.org

7, 49, 2401, 2401, 386561, 5764801, 58471553, 374712065, 4802079233, 149429406721, 1595702681601, 42091354378241, 665724390506497, 10190301669556225, 99086356274020353, 1654767311852142593, 14722487338708369409, 228161914444026740737, 2789435039707847196673
Offset: 1

Views

Author

N. J. A. Sloane, Jul 13 2015

Keywords

Comments

See Schut (1991) for precise definition.
Ignoring repetitions, the subsequence of A201919 of terms ending in 7 in base 14. - Eric M. Schmidt, Jul 18 2015

References

  • C. P. Schut, Idempotents. Report AM-R9101, Centrum voor Wiskunde en Informatica, Amsterdam, 1991.

Links

Crossrefs

Cf. A007185, A016090, A201919, A259986-A259991.

Programs

  • Sage
    def a(n) : return crt(1, 0, 2^n, 7^n) # Eric M. Schmidt, Jul 18 2015

Extensions

More terms from Eric M. Schmidt, Jul 18 2015
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.