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.

A216502 Indices of record values in A216476.

Original entry on oeis.org

1, 10, 11, 13, 14, 15, 18, 39, 59, 99, 106, 107, 147, 189, 999, 1049, 1059, 1199, 1399, 1599, 2999, 10669, 10679, 11789, 12799, 12899, 16779, 17899, 18899
Offset: 1

Views

Author

M. F. Hasler, Sep 11 2012

Keywords

Programs

  • PARI
    m=0;for(n=1,9e9,m<(m=max(A216476(n),m))&print1(n","))

Extensions

a(24)-a(29) from Charlie Neder, Feb 26 2019

A306564 Record values in A216476.

Original entry on oeis.org

1, 2, 4, 6, 10, 12, 18, 20, 28, 36, 48, 84, 132, 393, 657, 744, 1140, 1580, 2704, 3244, 8700, 12250, 17395, 17860, 19505, 36785, 59100, 67805, 97440
Offset: 1

Views

Author

Charlie Neder, Feb 26 2019

Keywords

Examples

			If we repeatedly apply the "Oware" operation to 11, we get the period-4 cycle - denoting the pivot digit with parentheses - (1)1 -> 0(2) -> 1(1) -> (2)0 -> (1)1 , and no number less than 11 has a cycle of this length or longer.

Crossrefs

Cf. A216476, A216502 (positions of records).

Formula

a(n) = A216476(A216502(n)).

A330760 a(n) is n transformed by the "successive Oware operation" (see the Comments and Example sections).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 32, 33, 43, 44, 54, 55, 20, 21, 31, 32, 42, 43, 53, 54, 64, 65, 21, 31, 32, 42, 43, 53, 54, 64, 65, 75, 31, 41, 42, 52, 53, 63, 64, 74, 75, 85, 41, 42, 52, 53, 63, 64, 74, 75, 85, 86, 51, 52, 62, 63, 73, 74, 84, 85, 95, 96, 52, 62, 63, 73, 74, 84, 85, 95, 96, 106, 62, 72
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Dec 29 2019

Keywords

Comments

To perform a "successive Oware operation" on n we must see the digits of n as a succession of numbers (539 is seen as the succession 5;3;9). We then replace the leftmost number of n with 0 and then "distribute" the (former) value of that number on all numbers, by increasing by 1 the following numbers ("wrapping" around, if necessary, to start over with the first number after the last has been increased). The same task is done with the second number of the result, then the third number of the last result, etc. until the rightmost number of the end result has been transformed. So, if n has k digits, the Oware operation will be done k times altogether.

Examples

			The Oware operation on 539 transforms first 539 into the numbers 5;3;9. It consists then of taking the 5 (and making this number zero) and then increase 5 times the subsequent numbers in a cyclic manner: 3->4; 9->10; 0->1; 4->5; 10->11, which yields the three numbers 1;5;11. The Oware operation is then repeated with 5 (the second number of the result) which turns 1;5;11 into 3;1;13. The last Oware operation is with 13, the rightmost number of the last result, which turns 3;1;13 into 8;5;4. Thus a(539) = 854.

Crossrefs

Cf. A216476 (number of iterations of the "Oware" operation until the initial position n is reproduced), A306564 (record values in A216476).
Showing 1-3 of 3 results.

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

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