A050278 -id:A050278 - cp's OEIS frontend

A171571 A050278/9, where A050278 are the pandigital numbers.

113717421, 113717422, 113717431, 113717433, 113717442, 113717443, 113717521, 113717522, 113717541, 113717544, 113717552, 113717554, 113717631, 113717633, 113717641, 113717644, 113717663, 113717664, 113717742, 113717743, 113717752

Offset: 1

Zak Seidov, Dec 12 2009

This is a finite sequence with 9*9! = 3265920 terms: a(9*9!) = 9876543210/9 = 1097393690. - Zak Seidov, Jan 14 2012

First differences are given in A217626. - M. F. Hasler, Sep 18 2017

Cf. A050278: Pandigital numbers, numbers containing the digits 0-9.

Cf. A217626.

(* first 720 terms: *) (1023000000 + FromDigits/@Permutations[{4,5,6,7,8,9}])/9

A204058 Largest integer m such that both m and n*m are decimal pandigital numbers (A050278).

Original entry on oeis.org

9876543210, 4938271605, 3291768054, 2469135780, 1975308642, 1645839027, 1409632875, 1234567890, 1097368245

Offset: 1

Zak Seidov, Jan 10 2012

Corresponding indices of a(n) in A050278 are 3265920, 1430987, 842972, 508475, 355944, 219427, 125670, 46234, 39091.

Also corresponding values of n*a(n) are 9876543210, 9876543210, 9875304162, 9876543120, 9876543210, 9875034162, 9867430125, 9876543120, 9876314205.

Cf. A050278, A203987, A204045.

A204532 Largest prime factors of zerofull restricted pandigital numbers A050278.

Original entry on oeis.org

5689, 1283, 113717431, 15683, 4919, 16245349, 113717521, 3344633, 5415121, 80309, 546719, 71341, 37905877, 113717633, 277, 28429411, 1006351, 6473, 8353, 393487, 18679, 599, 1403923, 693401, 113718421, 56859211, 113718431, 17827, 56859221, 2145631, 37906207

Offset: 1

Zak Seidov, Jan 16 2012

Largest term is a(3265903)=1097393447.

In defense of this sequence, let me say that when one is studying a sequence for which no formula or recurrence is known, one line of attack is to look at the largest prime factors of the terms. This might reveal some hidden property, or suggest a connection with a different sequence. - N. J. A. Sloane, Jan 17 2012

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A050278, A178775.

A257913 Pandigital numbers reordered so that the numbers A050278(n)/(2^k*3^m), where 2^k||A050278(n) and 3^m||A050278(n), appear in nondecreasing order.

Original entry on oeis.org

2845310976, 1379524608, 1745960832, 6398410752, 3076521984, 5892341760, 2305179648, 3718250496, 1578369024, 9145036728, 5392687104, 1356709824, 1607952384, 3215904768, 1485029376, 5638470912, 5619843072, 6185973240, 5234098176, 7246198035, 1072963584

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, May 12 2015

If two such numbers A050278(n_1)/(2^k_1*3^m_1) and A050278(n_2)/(2^k_2*3^m_2) are equal, then A050278(n_1) appears earlier than A050278(n_2) iff A050278(n_1)<A050278(n_2). For example, a(2)/(2^13*3^7)=a(3)/(2^7*3^11)= 77. There are 210189 such pairs.

Note that, a(1) = 2845310976 means that min(A050278(n)/(2^k*3^m)) = 2845310976/(2^19*3^4) = 67.

Cf. A050278, A257893, A257899, A257901, A257914, A065330.

A257914 Pandigital numbers reordered so that the numbers A050278(n)/(2^k*5^m), where 2^k||A050278(n) and 5^m||A050278(n), appear in nondecreasing order.

Original entry on oeis.org

3076521984, 1342968750, 3718250496, 6398410752, 1304296875, 1437890625, 3142968750, 1824609375, 3649218750, 9123046875, 1542389760, 1923046875, 1683947520, 1384906752, 2769813504, 2845310976, 1578369024, 3104296875, 1269843750, 6349218750, 1074659328

Offset: 1

Vladimir Shevelev and Peter J. C. Moses, May 12 2015

If two such numbers A050278(n_1)/(2^k_1*5^m_1) and A050278(n_2)/(2^k_2*5^m_2) are equal, then A050278(n_1) appears earlier than A050278(n_2) iff A050278(n_1)<A050278(n_2). For example, a(8)/(2^0*5^8)=a(9)/(2^1*5^8)= 4671. There are 234710 such pairs.

Note that, a(1) = 3076521984 means that min(A050278(n)/(2^k*5^m)) = 3076521984/(2^21*5^0) = 1467.

Cf. A050278, A257893, A257899, A257901, A257913.

A292471 Primes that do not divide any 10-digit pandigital number (i.e. any value in A050278).

Original entry on oeis.org

111119, 123457, 178889, 199999, 224467, 246913, 325477, 333337, 333367, 333667, 336667, 345679, 359147, 361909, 387403, 394549, 411113, 419753, 443221, 444449, 449161, 470551, 473219, 476647, 476659, 504323, 506173, 509053, 512683, 513269, 514289, 514357

Offset: 1

David J. Seal, Sep 21 2017

This is the complement in A000040 of the finite list of primes that divide one or more 10-digit pandigital numbers. That finite list has been obtained by computer; it contains 1102173 primes, with the first prime that is not in the list being prime(10545) = 111119 and the last that is in the list being prime(55537259) = 1097393447.

			a(1) = 111119 because 111119 is prime and does not divide any of the 10-digit pandigital numbers 1023456789, 1023456798, ..., 9876543210, and all smaller primes do divide at least one of them.

Cf. A050278, A061604, A180489, A274328, A292703.

A292703 Values of n such that prime(n) does not divide any 10-digit pandigital number (i.e. any value in A050278).

Original entry on oeis.org

10545, 11602, 16237, 17984, 19978, 21788, 28046, 28666, 28669, 28693, 28928, 29629, 30698, 30896, 32869, 33438, 34699, 35373, 37198, 37300, 37639, 39273, 39477, 39755, 39756, 41859, 42003, 42219, 42490, 42538, 42619, 42624

Offset: 1

David J. Seal, Sep 21 2017

This is the complement of the finite list of n such that prime(n) divides one or more 10-digit pandigital numbers. That finite list has been obtained by computer; it contains 1102173 numbers, with the first number that is not in the list being 10545 and the last that is in the list being 55537259.
A292471 is the corresponding list of primes.
These are the values of n for which A180489(n) has more than 10 digits, and also the values of n for which A274328(n) = 0.

			a(1) = 10545 because prime(10545) = 111119 does not divide any of the 10-digit pandigital numbers 1023456789, 1023456798, ..., 9876543210, and all smaller primes do divide at least one of them.

Cf. A050278, A061604, A180489, A274328, A292471.

A180618 The next smallest pandigital multiple of the pandigital number A050278(n).

Original entry on oeis.org

2046913578, 10234567980, 2046913758, 10234568970, 10234569780, 10234569870, 2046915378, 10234576980, 2046915738, 10234578960, 10234579680, 10234579860, 2046917358, 10234586970, 2046917538, 10234587960, 10234589670, 10234589760

Offset: 1

Lekraj Beedassy, Sep 12 2010

The smallest number of the form k*A050278(n), k>=2, which is in A171102.

Cf. A051018, A051019, A051020

Keyword:base and 2 different pandigital definitions introduced by R. J. Mathar, Oct 06 2010

A204085 Consider integers m such that both m and 2m are decimal pandigital numbers (A050278). The sequence gives indices of m in A050278.

Original entry on oeis.org

1, 3, 7, 9, 13, 15, 25, 27, 31, 33, 37, 39, 49, 51, 55, 57, 61, 63, 73, 75, 79, 81, 85, 87, 153, 155, 156, 157, 163, 166, 177, 179, 180, 181, 187, 190, 193, 195, 217, 219, 226, 232, 273, 275, 276, 277, 283, 286, 297, 299, 300, 301, 307, 310, 313, 315, 337

Offset: 1

Zak Seidov, Jan 10 2012

The sequence consists of 184320 terms, the last is a(184320) = 1430987 and the largest m = A050278(1430987) = 4938271605 and corresponding 2m = A050278(3265920) = 9876543210 the largest decimal pandigital number.

Cf. A050278, A203987, A204045, A204058.

A210014 Pandigital numbers (A050278) with each product of four adjacent digits visible as a substring of the digits.

Original entry on oeis.org

4327059168, 4613590728, 4613590872, 7860241359, 7860291354, 8490536127, 8760241359, 8760291354

Offset: 1

N. J. A. Sloane, Mar 16 2012

Computed by Jean-Marc Falcoz.

			Example for 4327059168: 4*3*2*7= 168; 5*9*1*6=270; 9*1*6*8=432 are substrings.

Eric Angelini, 10 different digits, 9 products
E. Angelini, 10 different digits, 9 products [Cached copy, with permission]

A generalization of A198298. Cf. A210013-A210020, A203569, A203566.

cp's OEIS Frontend

A171571 A050278/9, where A050278 are the pandigital numbers.

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A204058 Largest integer m such that both m and n*m are decimal pandigital numbers (A050278).

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A204532 Largest prime factors of zerofull restricted pandigital numbers A050278.

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A257913 Pandigital numbers reordered so that the numbers A050278(n)/(2^k*3^m), where 2^k||A050278(n) and 3^m||A050278(n), appear in nondecreasing order.

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A257914 Pandigital numbers reordered so that the numbers A050278(n)/(2^k*5^m), where 2^k||A050278(n) and 5^m||A050278(n), appear in nondecreasing order.

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A292471 Primes that do not divide any 10-digit pandigital number (i.e. any value in A050278).

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A292703 Values of n such that prime(n) does not divide any 10-digit pandigital number (i.e. any value in A050278).

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A180618 The next smallest pandigital multiple of the pandigital number A050278(n).

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A204085 Consider integers m such that both m and 2m are decimal pandigital numbers (A050278). The sequence gives indices of m in A050278.

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A210014 Pandigital numbers (A050278) with each product of four adjacent digits visible as a substring of the digits.

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