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 1-6 of 6 results.

A088868 Numbers n which are divisors of the number formed by concatenating (n-4), (n-3), (n-2) and (n-1) in that order.

Original entry on oeis.org

49, 109, 307121, 3837881, 415922011, 44886856951, 73071640562111, 11741452251865261, 138599925259848671
Offset: 1

Views

Author

Chuck Seggelin, Oct 20 2003

Keywords

Comments

Each member of this sequence appears to also be a factor of the number formed by concatenating (n+4), (n+3), (n+2) and (n+1) in that order. When evaluating concat((n+4),(n+3),(n+2),(n+1)) - concat((n-4),(n-3),(n-2),(n-1)) for members of this sequence the difference appears to always be a number of the form 8(0)...6(0)...4(0)...2 with the same number of zeros following the 8, 6 and 4. The member will be a factor of this number. Terms for this sequence can be produced by factoring numbers of this form. Let z=the number of zeros in one of the segments of a number d of the form 8(0)...6(0)...4(0)...2. Find the divisors of d. All divisors which are not of length z+1 are not members of this sequence and those that are of length z+1 are possible candidates and should be tested. For example let d = 8000000000000000006000000000000000004000000000000000002. z=17. The divisors of d are numerous, but only two are z+1 (18) digits long: 138599925259848671 and 27719985051 9697342. Testing these candidates confirms that the first one is a member of this sequence.
No more terms < 10^29. - David Wasserman, Aug 26 2005

Examples

			a(2)=109 because 109 is a factor of 105106107108.

Crossrefs

Cf. A069860, A088797, A088798, A088799, A088800.

A088870 Numbers n which are divisors of the number produced by concatenating (n-5), (n-4), ... (n-1) in that order.

Original entry on oeis.org

13677, 14647, 21291, 29567, 43941, 69031, 88701, 105991, 126507, 317973, 156304482823, 468913448469, 21729950852487, 2212933498428421, 6638800495285263, 12049739358792173, 36149218076376519, 11316117499289108644863
Offset: 1

Views

Author

Chuck Seggelin, Oct 20 2003

Keywords

Examples

			a(1)=13677 because 13677 is a factor of 1367213673136741367513676.

Crossrefs

Cf. A069860, A088797, A088798, A088799, A088800, A088868, A088869, A088871, A088872.

Extensions

More terms from David Wasserman, Aug 26 2005

A088872 Numbers n which are divisors of the number produced by concatenating (n-10), (n-9), (n-8), ... (n-1) in that order.

Original entry on oeis.org

37, 1793, 12247, 13061, 12345679, 17675669, 59454523, 10035074789, 11207086103, 12174047803, 13606288721, 14036302277, 17989804447, 19541987747, 20070727459, 21841045129, 22431989513, 23140930781, 32217871691
Offset: 1

Views

Author

Chuck Seggelin, Oct 20 2003

Keywords

Examples

			a(1)=37 because 37 is a factor of 27282930313233343536.

Crossrefs

Cf. A069860, A088797, A088798, A088799, A088800, A088868, A088869, A088870, A088871.

Extensions

More terms from David Wasserman, Aug 25 2005

A088869 Numbers n which are divisors of the number produced by concatenating (n-1), (n-2), ... (n-5) in that order.

Original entry on oeis.org

5, 15, 197, 591, 599, 985, 23363, 70089, 182415, 32533013, 97599039, 200814277564911, 334690462608185, 100208875079675883, 119690233947031245, 120541110603088381, 152213696825889183, 167014791799459805
Offset: 1

Views

Author

Chuck Seggelin, Oct 20 2003

Keywords

Examples

			a(2)=15 because 15 is a factor of 1413121110.

Crossrefs

Cf. A069860, A088797, A088798, A088799, A088800, A088868, A088870, A088871, A088872.

Extensions

More terms from David Wasserman, Aug 26 2005

A088871 Numbers n which are divisors of the number produced by concatenating (n-1), (n-2), ... (n-10) in that order.

Original entry on oeis.org

10, 22, 55, 181, 190, 362, 905, 2035, 4070, 10490, 11203, 14686, 17833, 22406, 23065, 35666, 36715, 46130, 56015, 73430, 78421, 89165, 100705, 201410, 1004530, 1093165, 1425313, 1480309, 1695710, 1956190, 2186330, 2850626, 2882707
Offset: 1

Views

Author

Chuck Seggelin, Oct 20 2003

Keywords

Examples

			a(2)=22 because 22 is a factor of 21201918171615141312.

Crossrefs

Cf. A069860, A088797, A088798, A088799, A088800, A088868, A088869, A088870, A088872.

Extensions

More terms from David Wasserman, Aug 26 2005

A088885 Minimum number of consecutive previous nonnegative integers to n that must be concatenated together in descending order such that n divides the concatenated term, or zero if n divides no such concatenation.

Original entry on oeis.org

1, 2, 2, 2, 5, 2, 0, 6, 8, 10, 0, 6, 0, 8, 5, 4, 2, 8, 3, 0, 0, 10, 0, 12, 0, 0, 26, 16, 0, 20, 0, 20, 11, 2, 20, 8, 0, 0, 0, 20, 40, 20, 4, 32, 35, 46, 38, 20, 40, 0, 2, 0, 0, 26, 10, 20, 3, 0, 0, 20, 55, 0, 0, 52, 0, 32, 0, 44, 17, 20, 0, 36, 26, 0, 50, 52, 21, 38, 67, 20, 0, 0, 9, 20, 0, 4, 59
Offset: 1

Views

Author

Chuck Seggelin, Oct 29 2003

Keywords

Comments

Concatenation always begins at n-1 and cannot go further than n-n (zero). Hence the maximum value of a(n) is n.

Examples

			a(8) = 6 because will divide the number formed by concatenating the 6 integers prior to 8 in descending order (i.e. 765432). 8 will not divide any lesser number of previous terms concatenated together beginning with 7 (i.e. 8 will not divide 7, 76, 765, 7654, or 76543). a(7) = 0 because 7 will not divide 6, 65, 654, 6543, 65432, 654321, or 6543210.

Crossrefs

Cf. A088798, A088800, A088869, A088871, A088886.
Showing 1-6 of 6 results.

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