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.

A075903 Duplicate of A029942.

Original entry on oeis.org

0, 1, 4, 5, 6, 9, 10, 24, 25, 32, 40, 49, 50, 51, 56, 60, 75, 76, 90, 99, 100, 125, 240, 249
Offset: 1

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Author

Keywords

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

A029943 Substring of both its square and its cube.

Original entry on oeis.org

0, 1, 5, 6, 10, 25, 50, 60, 76, 100, 250, 376, 500, 600, 625, 760, 1000, 2500, 3760, 5000, 6000, 6250, 7600, 9376, 10000, 25000, 37600, 50000, 60000, 62500, 76000, 90625, 93760, 100000, 109376, 250000, 376000, 500000, 600000, 625000
Offset: 1

Views

Author

Patrick De Geest

Keywords

Comments

Intersection of A018834 and A029942. - Reinhard Zumkeller, Feb 29 2012

Links

Programs

  • Haskell
    import Data.List (isInfixOf)
a029943 n = a029943_list !! (n-1)
a029943_list = filter f [0..] where
   f x = show x `isInfixOf` show (x^2) && show x `isInfixOf` show (x^3)
-- Reinhard Zumkeller, Nov 26 2011
  • Mathematica
    ssscQ[n_]:=Module[{idn=IntegerDigits[n],sq=IntegerDigits[n^2], cu=IntegerDigits[n^3],len=IntegerLength[n]},MemberQ[Partition[ sq,len,1], idn] &&MemberQ[Partition[cu,len,1],idn]]; Join[{0}, Select[Range[700000],ssscQ]] (* Harvey P. Dale, Apr 24 2011 *)

Formula

a(n) = A003226(m) * 10^k for appropriate m and k. [Reinhard Zumkeller, Nov 26 2011]

Extensions

Offset corrected by Reinhard Zumkeller, Nov 26 2011

A075904 Numbers k such that k^4 has k as a substring of its decimal expansion.

Original entry on oeis.org

0, 1, 5, 6, 10, 25, 50, 60, 76, 83, 92, 100, 107, 211, 217, 250, 352, 363, 376, 500, 556, 600, 625, 636, 760, 863, 909, 935, 1000, 1531, 1636, 2263, 2500, 2503, 3630, 3760, 4342, 5000, 5001, 6000, 6250, 7245, 7600, 8578, 9350, 9376, 10000, 25000, 28206, 32213
Offset: 1

Views

Author

Zak Seidov, Sep 27 2002

Keywords

Examples

			6^4 = 129_6, 83^4 = 4745_83_21, 2503^4 = 39_2503_37770081.

Links

Crossrefs

Cf. A018834 (squares), A029942 (cubes), A075905 (5th powers).

Programs

  • Mathematica
    Select[Range[10000], StringPosition[ToString[ #^4], ToString[ # ]] != {} &] (* Tanya Khovanova, Oct 11 2007 *)
ssQ[n_]:=Module[{idn=IntegerDigits[n],idn4=IntegerDigits[n^4]}, MemberQ[ Partition[ idn4, Length[ idn],1], idn]]; Select[Range[10000],ssQ] (* Harvey P. Dale, Mar 13 2013 *)
  • Python
    A075904_list, m = [0], [24, -36, 14, -1, 0]
for n in range(1,10**9+1):
    for i in range(4):
        m[i+1] += m[i]
    if str(n) in str(m[-1]):
        A075904_list.append(n) # Chai Wah Wu, Nov 05 2014

Extensions

More terms from Tanya Khovanova, Oct 11 2007
Added 0 to sequence by Chai Wah Wu, Nov 05 2014

A075905 Numbers k such that k^5 has k as a substring of its representation.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 18, 20, 24, 25, 30, 32, 40, 43, 45, 48, 49, 50, 51, 57, 60, 68, 70, 73, 75, 76, 80, 90, 93, 99, 100, 101, 125, 178, 192, 193, 195, 200, 205, 240, 249, 250, 251, 300, 307, 320, 375, 376, 400, 430, 432, 443, 480, 490, 499, 500, 501
Offset: 1

Views

Author

Zak Seidov, Sep 27 2002

Keywords

Examples

			45^5 = 18_45_28125, 3637^5 = 6_3637_9975073041957, 3975^5 = 992_3975_07802734375.

Links

Crossrefs

Cf. A018834 (squares), A029942 (cubes), A075904 (4th powers).

Programs

  • Mathematica
    Select[Range[0,600],SequenceCount[IntegerDigits[#^5],IntegerDigits[#]]>0&] (* Harvey P. Dale, Jul 06 2025 *)
  • Python
    A075905_list, m = [0], [120, -240, 150, -30, 1, 0]
for n in range(1,10**8+1):
    for i in range(5):
        m[i+1] += m[i]
    if str(n) in str(m[-1]):
        A075905_list.append(n) # Chai Wah Wu, Nov 05 2014

A115739 n is prime and digits of n^3 include digits of n as substring.

Original entry on oeis.org

5, 251, 499, 751, 1249, 4999, 8089, 18229, 31249, 49999, 281249, 4218751, 4999999, 9590417, 31622777, 68171507, 74218751, 574218751, 5740883989, 8829261293
Offset: 1

Views

Author

Giovanni Resta, Jan 30 2006

Keywords

Comments

Subset of A029942.

Examples

			751^3 = 423564_751.

Crossrefs

Cf. A029942, A115738.

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

A295900 Numbers n such that n^3 contains the consecutive substring 2,3,5,7.

Original entry on oeis.org

1331, 3108, 3176, 4093, 4643, 5846, 6178, 6797, 9175, 10731, 13076, 13245, 13309, 13310, 14093, 14526, 16291, 17852, 20095, 20791, 21835, 23635, 23766, 24093, 28452, 28672, 28673, 28674, 28675, 29211, 31080, 31760, 33907, 34093, 34986, 36449, 38538, 38599, 39526
Offset: 1

Views

Author

K. D. Bajpai, Nov 29 2017

Keywords

Examples

			1331 is in the sequence because 1331^3 = 2357947691 contains substring of prime digits "2357".
3108 is in the sequence because 3108^3 = 30022235712 contains substring of prime digits "2357".

Links

Crossrefs

Cf. A018834, A029942, A085823.

Programs

  • Mathematica
    Select[Range[100000], MemberQ[Partition[IntegerDigits[#^3], 4, 1], {2, 3, 5, 7}] &]
  • PARI
    isok(n) = {c = n^3; ret = 0; while (c > 1, if ((c % 10000) == 2357, ret = 1; break); c = floor(c/10);); return (ret);} \\ Michel Marcus, Dec 15 2017
  • Python
    A295900_list = [n for n in range(1,10**6) if '2357' in str(n**3)] # Chai Wah Wu, Feb 09 2018
Showing 1-8 of 8 results.

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