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.

A080463 Sum of the two numbers formed by alternate digits of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15, 16
Offset: 0

Views

Author

Amarnath Murthy, Mar 02 2003

Keywords

Comments

First 99 terms match with those of A007953.
They also match A209685. - M. F. Hasler, Jan 10 2016

Examples

			a(132546) = 124 + 356 = 480.

Links

Crossrefs

Cf. A007953, A080464, A080465.

Programs

  • Maple
    f:= proc(n) option remember; n mod 10 + (floor(n/10) mod 10) + 10*procname(floor(n/100)) end proc:
f(0):= 0:
seq(f(n),n=0..1000); # Robert Israel, Jan 10 2016
  • PARI
    A080463(n)=abs(vector(#n=digits(n),j,10^((#n-j)\2))*n~) \\ M. F. Hasler, Jan 10 2016

Formula

From Robert Israel, Jan 10 2016: (Start)
f(n) = n mod 10 + floor(n/10) mod 10 + 10*f(floor(n/100)).
G.f. G(x) satisfies G(x) = (x + 2x^2 + ... + 9x^9)/(1-x^10) + (x^10 + 2 x^20 + ... + 9 x^90)/((1-x)(1+x^10+...+x^90) + 10 (1 + x + ... + x^99) G(x^10).
(End)

Extensions

More terms from Ray Chandler, Oct 11 2003
Extended to offset 0 and b-file by M. F. Hasler, Jan 10 2016

A209674 For each n, define a sequence of numbers by S(0)=n, S(i) = sum of last two digits of the concatenation S(0)S(1)S(2)...S(i-1); a(n) = smallest m such that S(m) = 5, or -1 if 5 is never reached.

Original entry on oeis.org

-1, 4, 9, 9, 5, 0, 4, 3, 10, 11, 5, 3, 2, 6, 1, 5, 8, 7, 9, 6, 10, 7, 8, 1, 7, 4, 3, 10, 6, 4, 10, 2, 1, 8, 5, 8, 7, 6, 4, 3, 6, 1, 4, 7, 4, 3, 6, 4, 3, 7, 1, 9, 11, 5, 8, 6, 4, 3, 7, 2, 5, 8, 7, 4, 6, 4, 3, 7, 2, 6, 4, 10, 5, 6, 4, 3, 7, 2, 6, 9, 11, 7, 6, 4, 3, 7, 2, 6, 9, 8, 12, 6, 4, 3, 7, 2, 6, 9, 8, 10
Offset: 0

Views

Author

N. J. A. Sloane, Mar 11 2012

Keywords

Comments

a(n) = -1 iff n ends in 00 (e.g. 100, 200, ...). (It is sufficient to check the 100 starts i,j, 0 <= i, j <= 9.)
5 is the unique number common to the trajectories of all numbers from 1 to 99.
Iterate the map k -> A209685(k), starting at n, until reaching 5, or -1 if 5 is never reached.

Examples

			For n=4 we have S(0)=4, S(1)=4, S(2)=8, S(3)=12, S(4)=3, S(5)=5, so a(4)=5.

References

  • Eric Angelini, Posting to Math Fun Mailing List, Mar 11 2012.

Crossrefs

Cf. A209685, A209686.

Programs

Formula

The sequence is ultimately periodic.

Extensions

Corrected and extended by Charles R Greathouse IV, Mar 11 2012

A336716 Lexicographically earliest sequence of distinct positive integers such that the sum of the last two digits of the sequence starts the new term.

Original entry on oeis.org

1, 2, 3, 5, 8, 13, 4, 7, 11, 20, 21, 30, 31, 40, 41, 50, 51, 6, 70, 71, 80, 81, 9, 10, 12, 32, 52, 72, 90, 91, 101, 14, 53, 82, 102, 22, 42, 60, 61, 73, 103, 33, 62, 83, 110, 15, 63, 92, 111, 23, 54, 93, 120, 24, 64, 104, 43, 74, 112, 34, 75, 121, 35, 84, 122, 44, 85, 130, 36, 94, 131, 45, 95, 140, 46, 105, 55, 106
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Aug 01 2020

Keywords

Comments

No term ending with two or more zeros is part of the sequence as the next term would start with zero.

Examples

			5 + 8 = 13; now the last two digits of the sequence are 1 and 3; their sum is 4; the last two digits of the sequence are now 3 and 4; their sum is 7; the last two digits are now 4 and 7 with sum 11; those two digits sum up to 2 but as 2 is already in the sequence we extend it with 20 as 20 is the smallest integer starting with the sum 2 that is not yet in the sequence.

Links

Crossrefs

Cf. A209685.
Showing 1-3 of 3 results.

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

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