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.

A277054 Least k such that n-th repunit times k is a pandigital.

Original entry on oeis.org

1023456789, 93125079, 9222117, 1110789, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115, 92115
Offset: 1

Views

Author

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

Keywords

Comments

Starting from n=5, a(n)=A277056(10)=92115, and the corresponding pandigitals are 1023499...989765 (n-5 nines).
a(1)-a(5) constitute row 10 of A277055.
a(n)*A002275(n) is 1023456789, 1024375869, 1023654987, 1234086579, 1023489765, ...

Examples

			a(2) = 93125079 because A002275(2)*93125079 = 11*93125079 = 1024375869 that is a pandigital and 93125079 is the least number with this property.

Crossrefs

Cf. A002275, A171102, A277055, A277056, A277057.

A277056 Least k such that any sufficiently long repunit multiplied by k is a pandigital number in numerical base n.

Original entry on oeis.org

2, 5, 7, 34, 195, 727, 3724, 9124, 92115, 338161, 2780514, 6871290, 99000993
Offset: 2

Views

Author

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

Keywords

Comments

Trailing terms of rows of A277055.
Written in base n, the terms read: 10, 12, 13, 114, 523, 2056, 7214, 13457, 92115, 21107A, B21116, 156776A, D211117, ...

Examples

			Any binary repunit multiplied by 2 is a binary pandigital, so a(2)=2 (10 in binary).
k-th decimal repunit for k>4 multiplied by 92115 gives a decimal pandigital number (see A277054) with no number less than 92115 having the same property, so a(10)=92115.

Crossrefs

Cf. A002275, A171102, A277054, A277055, A277059.

Formula

Conjecture: for even n>4, a(n) = (n-2)*n^(n/2-1) + n^(n/2-2) + (n^(n/2)-1)/(n-1) + n/2 - 1.

A277058 Irregular array by rows: A(n,m) is the least number which gives a number containing all nonzero digits when multiplied by m-th repunit for base n; each row is truncated when reaches its stationary point.

Original entry on oeis.org

1, 5, 4, 27, 6, 194, 33, 14, 1865, 425, 45, 22875, 17603, 403, 370, 342391, 38094, 8631, 588, 6053444, 605410, 67228, 7385, 3364, 123456789, 11225079, 1113198, 210789, 11115, 2853116705
Offset: 2

Views

Author

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

Keywords

Comments

For row n, the initial number is A023811(n) and the trailing number is A277059(n). Row 10 is A277057(1)-A277057(5) [note that the initial row is row 2].

Examples

			The first rows of the array are:
1, (1, 1...)
5, 4, (4, 4...)
27, 6, (6, 6...)
194, 33, 14,
1865, 425, 45,
22875, 17603, 403, 370,
342391, 38094, 8631, 588,
6053444, 605410, 67228, 7385, 3364,
123456789, 11225079, 1113198, 210789, 11115

Crossrefs

Cf. A002275, A023811, A277055, A277057, A277059.
Showing 1-3 of 3 results.

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

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