A277057 -id:A277057 - cp's OEIS frontend

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

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

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

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, ...

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

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

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

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

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].

			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

Cf. A002275, A023811, A277055, A277057, A277059.

A277059 Least k such that any sufficiently long repunit multiplied by k contains all nonzero digits in base n.

Original entry on oeis.org

1, 4, 6, 14, 45, 370, 588, 3364, 11115, 168496, 271458, 2442138

Offset: 2

Andrey Zabolotskiy and Altug Alkan, Sep 26 2016

Trailing terms of rows of A277058.

Written in base n, the terms read: 1, 11, 12, 24, 113, 1036, 1114, 4547, 11115, 105659, 111116, 67676A, ...

			Any binary repunit itself contains a 1, so a(2)=1.
k-th decimal repunit for k>4 multiplied by 11115 contains all nonzero decimal digits (see A277057) with no number less than 11115 having the same property, so a(10)=11115.

Cf. A002275, A277056, A277057, A277058.

Conjecture:
for n=2m, a(n) = (n^m-1)/(n-1) + m - 1;
for n=4m+1, a(n) = (n^(2m)-1)(n^2+1) / (2(n^2-1)) + m;
for n=4m-1, a(n) = (n^(2m-2)-1)(n^2+1) / (2(n^2-1)) + m + n^(2m-1).

cp's OEIS Frontend

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

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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.

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A277059 Least k such that any sufficiently long repunit multiplied by k contains all nonzero digits in base n.

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