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 1-7 of 7 results.

A032740 Numbers k such that k is a substring of 2^k.

Original entry on oeis.org

6, 10, 35, 36, 37, 44, 49, 51, 60, 67, 72, 73, 82, 85, 89, 93, 179, 188, 190, 191, 226, 234, 252, 297, 312, 321, 356, 373, 391, 425, 429, 430, 438, 445, 451, 475, 478, 479, 486, 516, 519, 521, 526, 549, 551, 581, 582, 583, 598, 601, 603, 609, 613, 619, 627, 632, 642, 652, 653, 655, 660
Offset: 1

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Author

Patrick De Geest, May 15 1998

Keywords

Examples

			2^93 = 99035203142830421991929_93_792.
		

Crossrefs

Programs

  • Haskell
    import Data.List (isInfixOf)
    a032740 n = a032740_list !! (n-1)
    a032740_list = [x | x <- [0..], show x `isInfixOf` (show $ 2 ^ x)]
    -- Reinhard Zumkeller, Jan 19 2014
  • Mathematica
    d[n_] := IntegerDigits[n]; parQ[n_] := MemberQ[Partition[d[2^n], Length[x = d[n]], 1], x]; Select[Range[660], parQ] (* Jayanta Basu, Jun 17 2013 *)
    Select[Range[700],SequenceCount[IntegerDigits[2^#],IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 10 2019 *)

A049301 Numbers k such that k is a substring of 3^k.

Original entry on oeis.org

7, 9, 24, 28, 57, 61, 62, 69, 71, 72, 77, 78, 80, 83, 87, 89, 95, 111, 162, 170, 174, 185, 191, 218, 222, 225, 229, 232, 249, 255, 259, 266, 267, 286, 288, 298, 314, 315, 322, 328, 329, 330, 332, 338, 351, 352, 362, 373, 376, 381, 386, 387, 414, 421, 435, 438
Offset: 1

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Keywords

Crossrefs

Programs

  • Mathematica
    ssQ[n_]:=MemberQ[Partition[IntegerDigits[3^n],IntegerLength[n],1], IntegerDigits[ n]]; Select[Range[500],ssQ] (* Harvey P. Dale, Jul 16 2013 *)

A049302 Numbers k such that k is a substring of 4^k.

Original entry on oeis.org

6, 10, 17, 25, 36, 42, 50, 59, 60, 61, 72, 73, 78, 79, 81, 84, 86, 87, 89, 92, 93, 95, 96, 160, 200, 212, 222, 225, 227, 239, 260, 261, 269, 290, 291, 296, 300, 301, 304, 311, 313, 315, 324, 326, 327, 330, 336, 344, 345, 348, 350, 355, 362, 372, 378, 379, 381
Offset: 1

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Author

Keywords

Crossrefs

A049304 Numbers k such that k is a substring of 6^k.

Original entry on oeis.org

6, 7, 9, 13, 21, 22, 23, 29, 39, 40, 42, 44, 45, 48, 53, 55, 56, 60, 63, 64, 65, 67, 68, 69, 70, 73, 74, 75, 76, 77, 79, 82, 83, 87, 89, 92, 93, 94, 98, 105, 107, 127, 129, 131, 134, 137, 143, 147, 152, 163, 165, 167, 174, 179, 184, 189, 197, 224, 226, 227, 234, 240
Offset: 1

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Author

Keywords

Examples

			9 is in the sequence because 6^9 = 10077696 contains 9 as a substring. - _David A. Corneth_, Aug 13 2021
		

Crossrefs

Programs

  • Mathematica
    Select[Range[250],SequenceCount[IntegerDigits[6^#],IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 03 2018 *)
  • PARI
    is(n) = { my(digs6n, digsn, streak, i, j); digs6n = digits(6^n); digsn = digits(n); for(i = 1, #digs6n + 1 - #digsn, streak = 0; for(j = 1, #digsn, if(digs6n[i + j - 1] == digsn[j], streak++ , next(2) ) ); if(streak == #digsn, return(1) ) ); 0 } \\ David A. Corneth, Aug 13 2021
  • Python
    def ok(n): return str(n) in str(6**n)
    print(list(filter(ok, range(241)))) # Michael S. Branicky, Aug 13 2021
    

A049306 Numbers k such that k is a substring of 8^k.

Original entry on oeis.org

4, 6, 7, 10, 13, 17, 18, 28, 31, 33, 36, 38, 42, 44, 47, 48, 49, 52, 54, 56, 58, 60, 63, 64, 67, 68, 69, 76, 77, 79, 81, 82, 83, 85, 86, 89, 90, 91, 94, 97, 112, 115, 124, 130, 135, 165, 173, 176, 178, 189, 193, 195, 206, 208, 215, 221, 225, 249, 251, 252, 253, 256
Offset: 1

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    Select[Range[300],SequenceCount[IntegerDigits[8^#],IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 16 2018 *)
  • Python
    def ok(n): return str(n) in str(8**n)
    print(list(filter(ok, range(257)))) # Michael S. Branicky, Aug 13 2021

A049305 Numbers k such that k is a substring of 7^k.

Original entry on oeis.org

3, 4, 6, 8, 12, 15, 20, 40, 42, 43, 50, 53, 55, 59, 60, 61, 62, 69, 72, 73, 74, 75, 78, 79, 80, 81, 83, 86, 87, 88, 89, 93, 94, 95, 96, 97, 99, 100, 103, 111, 113, 114, 118, 164, 165, 185, 193, 200, 207, 210, 215, 220, 230, 232, 238, 241, 243, 250, 253, 254, 255
Offset: 1

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Author

Keywords

Crossrefs

Programs

  • Python
    def ok(n): return str(n) in str(7**n)
    print(list(filter(ok, range(256)))) # Michael S. Branicky, Aug 13 2021

A049307 Numbers k such that k is a substring of 9^k.

Original entry on oeis.org

5, 7, 9, 25, 26, 31, 37, 43, 46, 47, 48, 53, 59, 60, 61, 63, 68, 69, 70, 72, 74, 76, 80, 85, 87, 88, 89, 91, 94, 97, 101, 104, 107, 124, 132, 135, 140, 148, 158, 166, 170, 180, 187, 190, 199, 209, 211, 215, 231, 243, 244, 256, 266, 270, 271, 279, 283, 288, 289, 291
Offset: 1

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Author

Keywords

Crossrefs

Showing 1-7 of 7 results.