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 1-10 of 14 results. Next

A136492 Complement of A018826.

Original entry on oeis.org

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 01 2008

Keywords

Crossrefs

Cf. A018826, A136491.

Programs

  • Mathematica
    Select[Range[0, 100], StringFreeQ[IntegerString[#^2, 2], IntegerString[#, 2]] &] (* Paolo Xausa, Apr 05 2024 *)

A018834 Numbers k such that the decimal expansion of k^2 contains k as a substring.

Original entry on oeis.org

0, 1, 5, 6, 10, 25, 50, 60, 76, 100, 250, 376, 500, 600, 625, 760, 1000, 2500, 3760, 3792, 5000, 6000, 6250, 7600, 9376, 10000, 14651, 25000, 37600, 50000, 60000, 62500, 76000, 90625, 93760, 100000, 109376, 250000, 376000, 495475, 500000, 505025
Offset: 1

Views

Author

David W. Wilson

Keywords

Examples

			25^2 = 625 which contains 25.
3792^2 = 14_3792_64, 14651^2 = 2_14651_801.

Links

Crossrefs

Cf. A003226, A046831, A046851, A045953.
Cf. A000290. Supersequence of A029943.
Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018833 (base 9).
Cf. A029942 (cubes), A075904 (4th powers), A075905 (5th powers).

Programs

  • Haskell
    import Data.List (isInfixOf)
a018834 n = a018834_list !! (n-1)
a018834_list = filter (\x -> show x `isInfixOf` show (x^2)) [0..]
-- Reinhard Zumkeller, Jul 27 2011
  • Mathematica
    Select[Range[510000], MemberQ[FromDigits /@ Partition[IntegerDigits[#^2], IntegerLength[#], 1], #] &] (* Jayanta Basu, Jun 29 2013 *)
Select[Range[0,510000],StringPosition[ToString[#^2],ToString[#]]!={}&] (* Ivan N. Ianakiev, Oct 02 2016 *)
  • Python
    from itertools import count, islice
def A018834_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:str(n) in str(n**2), count(max(startvalue,0)))
A018834_list = list(islice(A018834_gen(),20)) # Chai Wah Wu, Apr 04 2023

A018827 Numbers n such that n is a substring of its square in base 3 (written in base 10).

Original entry on oeis.org

0, 1, 3, 7, 9, 27, 32, 43, 81, 131, 243, 287, 706, 729, 1330, 1390, 1679, 1832, 2187, 2899, 3848, 4170, 5234, 6436, 6561, 11544, 12510, 14261, 19308, 19683, 30433, 33181, 34135, 35203, 35323, 37530, 38669, 42783, 59049, 72070, 79583, 93539, 99543
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A018826 (base 2), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018833 (base 9), A018834 (base 10).

Programs

  • Mathematica
    Select[Range[0, 10^5], StringContainsQ[IntegerString[#^2, 3], IntegerString[#, 3]] &] (* Paolo Xausa, Apr 05 2024 *)
  • Python
    from sympy.ntheory import digits
def s(n, base=3): return "".join(map(str, digits(n, base)[1:]))
def ok(n): return s(n) in s(n**2)
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Apr 04 2024

A018828 Numbers n such that n is a substring of its square (both n and n squared in base 4) (written in base 10).

Original entry on oeis.org

0, 1, 4, 16, 41, 54, 64, 164, 165, 256, 290, 487, 545, 566, 1024, 1160, 1948, 2180, 3546, 4096, 4226, 4261, 7625, 8321, 8720, 9514, 13813, 13867, 15913, 16158, 16384, 16904, 33284, 46126, 54854, 55468, 63652, 64632, 65536, 66050, 67616, 113047, 130591
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A018826 (base 2), A018827 (base 3), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018833 (base 9), A018834 (base 10).

Programs

  • Mathematica
    Select[Range[0,150000],SequenceCount[IntegerDigits[#^2,4],IntegerDigits[#,4]]>0&] (* Harvey P. Dale, Aug 13 2023 *)

Extensions

Definition clarified by Harvey P. Dale, Aug 13 2023

A018829 Numbers n such that n is a substring of its square in base 5 (written in base 10).

Original entry on oeis.org

0, 1, 5, 14, 25, 38, 125, 349, 408, 543, 625, 3125, 4743, 5292, 10888, 12196, 13201, 15625, 25509, 26460, 36536, 43614, 55038, 57837, 78125, 136888, 207889, 219698, 234783, 390625, 445663, 1090347, 1098490, 1336564, 1437874, 1720752, 1915227
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018833 (base 9), A018834 (base 10).

Programs

  • Mathematica
    Select[Range[0,2*10^6],SequenceCount[IntegerDigits[ #^2,5],IntegerDigits[ #,5]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 04 2019 *)

A018830 Numbers n such that n is a substring of its square in base 6 (written in base 10).

Original entry on oeis.org

0, 1, 3, 4, 6, 9, 18, 24, 28, 36, 54, 81, 108, 136, 144, 168, 216, 324, 486, 648, 816, 864, 1008, 1216, 1296, 1944, 2916, 3888, 4896, 5184, 6048, 6458, 6561, 7296, 7776, 8451, 11664, 16768, 17496, 22779, 23328, 23985, 29376, 29889, 31104, 34299, 34549, 36288
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018829 (base 5), A018831 (base 7), A018832 (base 8), A018833 (base 9), A018834 (base 10).

Programs

  • Mathematica
    Select[Range[0, 10^5], StringContainsQ[IntegerString[#^2, 6], IntegerString[#, 6]] &] (* Paolo Xausa, Apr 05 2024 *)

A018831 Numbers n such that n is a substring of its square in base 7 (written in base 10).

Original entry on oeis.org

0, 1, 7, 30, 49, 285, 343, 911, 1900, 2208, 2401, 13962, 16807, 59763, 64098, 69128, 85880, 97734, 117649, 195032, 418341, 754422, 823543, 2162126, 2629229, 2790841, 3488518, 3842400, 4960401, 5764801, 7923812, 8559490, 15134882, 19765943, 31466333, 36415297
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018832 (base 8), A018833 (base 9), A018834 (base 10).

Programs

  • Mathematica
    Select[Range[0, 10^7], StringContainsQ[IntegerString[#^2, 7], IntegerString[#, 7]] &] (* Paolo Xausa, Apr 05 2024 *)

Extensions

a(35)-a(36) from Pontus von Brömssen, Apr 04 2024

A018832 Numbers n such that n is a substring of its square in base 8 (written in base 10).

Original entry on oeis.org

0, 1, 8, 27, 64, 283, 290, 512, 545, 1948, 2320, 4096, 4360, 8452, 13813, 16158, 16642, 23063, 26139, 27427, 27734, 32768, 33025, 67616, 87723, 110503, 129264, 130591, 133136, 184504, 206573, 226094, 262144, 264200, 526340, 701784, 1044728, 1050626
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018833 (base 9), A018834 (base 10).

Programs

  • Mathematica
    Select[Range[0, 10^6], StringContainsQ[IntegerString[#^2, 8], IntegerString[#, 8]] &] (* Paolo Xausa, Apr 05 2024 *)

A018833 Numbers n such that n is a substring of its square in base 9 (written in base 10).

Original entry on oeis.org

0, 1, 9, 32, 43, 81, 287, 706, 729, 4170, 6561, 30433, 37530, 38669, 42783, 59049, 99543, 192211, 281782, 394981, 415578, 531441, 561785, 666112, 1723076, 2046242, 3039924, 3485488, 4782969, 8684182, 11512384, 12684634, 18346925, 19988197, 29728486, 31190295
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018834 (base 10).

Programs

  • Mathematica
    Select[Range[0, 10^7], StringContainsQ[IntegerString[#^2, 9], IntegerString[#, 9]] &] (* Paolo Xausa, Apr 05 2024 *)

Extensions

a(35)-a(36) from Pontus von Brömssen, Apr 04 2024

A136490 Numbers whose binary representation is contained in that of their cubes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 23, 24, 28, 29, 30, 31, 32, 33, 34, 36, 39, 40, 41, 48, 56, 58, 60, 62, 63, 64, 65, 66, 68, 72, 80, 91, 96, 99, 111, 112, 115, 116, 120, 124, 126, 127, 128, 129, 130, 132, 136, 144, 160, 192, 222, 224, 230, 232
Offset: 1

Views

Author

Reinhard Zumkeller, Jan 01 2008

Keywords

Comments

Complement of A136491.
A136510(a(n)) <= 3 for n>0. - Reinhard Zumkeller, Jan 03 2008

Crossrefs

Cf. A018826 (squares), A029942 (base 10), A136491, A136510.

Programs

  • Mathematica
    Select[Range[0, 300], StringContainsQ[IntegerString[#^3, 2], IntegerString[#, 2]] &] (* Paolo Xausa, Apr 04 2024 *)
  • Python
    def ok(n): return bin(n)[2:] in bin(n**3)[2:]
print([k for k in range(250) if ok(k)]) # Michael S. Branicky, Apr 04 2024

Extensions

More terms from Reinhard Zumkeller, Jan 03 2008
Showing 1-10 of 14 results. Next

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

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