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 1-3 of 3 results.

A032764 Take list of odd numbers, move left digit of each term to end of previous term.

Original entry on oeis.org

1, 3, 5, 7, 9, 1, 11, 31, 51, 71, 92, 12, 32, 52, 72, 93, 13, 33, 53, 73, 94, 14, 34, 54, 74, 95, 15, 35, 55, 75, 96, 16, 36, 56, 76, 97, 17, 37, 57, 77, 98, 18, 38, 58, 78, 99, 19, 39, 59, 79, 91, 11, 31, 51, 71, 91, 111, 131, 151, 171, 191, 211, 231, 251, 271, 291, 311
Offset: 0

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Author

Patrick De Geest, May 15 1998

Keywords

Crossrefs

Programs

  • Haskell
    a032764 n = a032764_list !! n
    a032764_list = 1 : map read (zipWith (++) vs (tail us)) :: [Integer]
       where (us,vs) = unzip $ map ((splitAt 1) . show) [1, 3 ..]
    -- Reinhard Zumkeller, Oct 10 2013

A290148 a(n) is the integer resulting from the concatenation of the unit digit of n-1 to the digits of n without its own unit digit.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 91, 1, 11, 21, 31, 41, 51, 61, 71, 81, 92, 2, 12, 22, 32, 42, 52, 62, 72, 82, 93, 3, 13, 23, 33, 43, 53, 63, 73, 83, 94, 4, 14, 24, 34, 44, 54, 64, 74, 84, 95, 5, 15, 25, 35, 45, 55, 65, 75, 85, 96, 6, 16, 26, 36, 46, 56, 66, 76, 86, 97, 7
Offset: 1

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Author

Michel Marcus, Jul 21 2017

Keywords

Comments

Take list of integers n >= 1, move the right-most digit of each term to the start of the next term.
Every number appears, see A381225. - N. J. A. Sloane, Feb 23 2025

Examples

			For n=46, n-1 is 45, so a(46) is the concatenation of 5 (the unit digit of 45) and 4 (46 without 6), giving 54.
For n=123, n-1 is 122, so a(123) is the concatenation of 2 (the unit digit of 122) and 12 (123 without 3), giving 212.
		

Crossrefs

Programs

  • Maple
    f:= n -> (n-1 mod 10) * 10^ilog10(n) + floor(n/10);
  • PARI
    a(n) = my(precd = (n-1)%10); if (n < 10, precd, eval(concat(Str(precd), Str(n\10))));
    
  • Python
    def a(n): return 0 if n == 1 else int(str((n-1)%10)+ str(n)[:-1])
    print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Feb 22 2025

Formula

a(n) = (n-1 mod 10)*10^A004216(n) + floor(n/10). # Robert Israel, Jul 21 2017

A385116 Take the natural numbers, erase all occurrences of the digit "0," and shift all remaining digits leftward without changing the position of commas.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 21, 31, 41, 51, 61, 71, 81, 92, 21, 22, 23, 24, 25, 26, 27, 28, 29, 33, 13, 23, 33, 43, 53, 63, 73, 83, 94, 41, 42, 43, 44, 45, 46, 47, 48, 49, 55, 15, 25, 35, 45, 55, 65, 75, 85, 96, 61, 62, 63, 64, 65, 66, 67, 68, 69, 77
Offset: 1

Views

Author

Dominic McCarty, Jun 18 2025

Keywords

Comments

a(1) = 1; digit stream is the same as that of A004719 and digit lengths A055642(a(n)) = A055642(n).

Examples

			Starting with:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, ...
Erase all zeros:
1, 2, 3, 4, 5, 6, 7, 8, 9, 1_, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2_, 21, ...
Shift all remaining digits to the left:
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 21, 31, 41, 51, 61, 71, 81, 92, 21, 22, ...
		

Crossrefs

Programs

  • Python
    from itertools import count
    s = "".join(map(str,range(1,72))).replace("0","")
    a, i, = [], 0
    for k in count(1):
        if (j:=i+len(str(k))) > len(s): break
        a.append(int(s[i:j]))
        i = j
    print(a)
Showing 1-3 of 3 results.