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.

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A035933 Smallest number that takes n steps to reach 0 under "k->min product of 2 numbers whose concatenation is k".

Original entry on oeis.org

0, 1, 11, 26, 39, 77, 177, 359, 977, 1977, 3659, 13659, 28879, 128879, 289978, 999663, 4474997, 14474997, 39596964, 139596964, 389999999, 1389999999, 2899999999, 12899999999, 49999999986, 149999999986, 446874999996, 1446874999996
Offset: 0

Views

Author

Erich Friedman

Keywords

Comments

a(28) > 4.4*10^12. - Jon E. Schoenfield, Jan 05 2009

Crossrefs

Cf. A035930-A035935.

Extensions

More terms from Naohiro Nomoto, Apr 03 2001
a(18)-a(27) from Jon E. Schoenfield, Jan 05 2009

A347470 Least product of any two numbers whose concatenation is n, excluding 0*n for n > 9.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 0, 11, 12
Offset: 0

Views

Author

M. F. Hasler, Sep 03 2021

Keywords

Comments

Leading zeros are not allowed: e.g., 101 = concat(10,1) but not concat(1,01). Although 0 is a valid number, we don't allow the trivial decomposition n = concat(0, n) except for the single-digit n < 10, otherwise the minimal product would always be 0.
For n < 111, this sequence coincides with A035930 (same with "largest"), because there is only one possible concatenation, but it differs for n > 111, cf. examples.

Examples

			The number n = 112 is the concatenation of 1 and 12, or of 11 and 2, with respective products 1*12 = 12 and 11*2 = 22. Hence, a(112) = 12, while A035930(112) = 22.

Links

Crossrefs

Cf. A035930, A007954, A088117, A171765 and A257297.

Programs

  • PARI
    apply( {A347470(x,t(b,c)=if(c\10<=b%c,b\c*(b%c),c>10,oo))= if(x>9,vecmin(vector(logint(x,10),j,t(x,10^j))))}, [0..112])
Previous Showing 11-12 of 12 results.

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

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