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 1-5 of 5 results.

A082242 Multiples of 4 that are the concatenation of 4 consecutive natural numbers.

Original entry on oeis.org

3456, 9101112, 13141516, 17181920, 21222324, 25262728, 29303132, 33343536, 37383940, 41424344, 45464748, 49505152, 53545556, 57585960, 61626364, 65666768, 69707172, 73747576, 77787980, 81828384, 85868788, 89909192, 93949596, 979899100, 101102103104
Offset: 1

Views

Author

Amarnath Murthy, Apr 11 2003

Keywords

Comments

Except for the first term all the other terms are a concatenation of 4 numbers from 4k+1 to 4k+4. All the natural numbers are used except 1,2,7 and 8.

Crossrefs

Cf. A082243.

Programs

  • Mathematica
    Select[FromDigits[Flatten[IntegerDigits[#]]]&/@Partition[Range[100],4,1],Mod[#,4]==0&] (* Harvey P. Dale, Jun 16 2023 *)

Extensions

More terms from Harvey P. Dale, Jun 16 2023

A082247 Multiples of 7 that are concatenation of 7 consecutive natural numbers.

Original entry on oeis.org

3456789, 13141516171819, 20212223242526, 27282930313233, 34353637383940, 41424344454647, 48495051525354, 55565758596061, 62636465666768, 69707172737475, 76777879808182, 83848586878889, 90919293949596, 102103104105106107108, 109110111112113114115
Offset: 1

Views

Author

Amarnath Murthy, Apr 11 2003

Keywords

Comments

From 2nd terms onwards it is observed that if a(r) ends in k then a(r+1) begins with k+1. This is true up to the term 90919293949596. (Why?)

Links

Crossrefs

Cf. A082242, A082243, A082248.

Programs

  • Mathematica
    Select[FromDigits[Flatten[IntegerDigits[#]]]&/@Partition[Range[100],7,1],Divisible[ #,7]&] (* Harvey P. Dale, May 18 2021 *)

A082248 a(n) = A082247(n)/7.

Original entry on oeis.org

493827, 1877359453117, 2887460463218, 3897561473319, 4907662483420, 5917763493521, 6927864503622, 7937965513723, 8948066523824, 9958167533925, 10968268544026, 11978369554127, 12988470564228, 14586157729300872444, 15587158730301873445, 16588159731302874446
Offset: 1

Views

Author

Amarnath Murthy, Apr 11 2003

Keywords

Comments

From 2nd terms onwards some pattern is visible which would change when three or more digit numbers occur.

Crossrefs

Cf. A082242, A082243, A082247.

A082249 Reverse concatenation of 7 numbers that are multiples of 7.

Original entry on oeis.org

22212019181716, 29282726252423, 36353433323130, 43424140393837, 50494847464544, 57565554535251, 64636261605958, 71706968676665, 78777675747372, 85848382818079, 92919089888786, 99989796959493, 108107106105104103102
Offset: 1

Views

Author

Amarnath Murthy, Apr 11 2003

Keywords

Comments

It appears that if a(r) begins with k then a(r+1) ends in k+1. This is true up to the term 99989796959493.

Links

Crossrefs

Cf. A082242, A082243, A082247, A082248, A082250.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003

A082250 a(n) = A082249(n)/7.

Original entry on oeis.org

3173145597388, 4183246607489, 5193347617590, 6203448627691, 7213549637792, 8223650647893, 9233751657994, 10243852668095, 11253953678196, 12264054688297, 13274155698398, 14284256708499, 15443872300729157586
Offset: 1

Views

Author

Amarnath Murthy, Apr 11 2003

Keywords

Comments

Some pattern is visible which would change when numbers of three or more digits occur in A082249. Conjecture: If the concatenation of k consecutive r-digit numbers is divisible by n then the concatenation of the next k numbers would also be divisible by n provided it contains the same number of digits as the first number. This should be true for both forward and reverse concatenation.

Crossrefs

Cf. A082242, A082243, A082247, A082248, A082249.

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 19 2003
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.