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.

A275772 Average values of different permutations of digits of A275945(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 11, 22, 33, 44, 55, 22, 33, 44, 55, 66, 22, 33, 44, 55, 66, 33, 44, 55, 66, 77, 33, 44, 55, 66, 77, 44, 55, 66, 77, 88, 44, 55, 66, 77, 88, 55, 66, 77, 88, 99, 37, 74, 111, 148, 185, 222, 259, 296, 333, 370, 74, 111, 148, 185, 222, 259
Offset: 1

Views

Author

Altug Alkan, Aug 29 2016

Keywords

Examples

			a(10) = 11 because A275945(10) = 11.
a(11) = 22 because A275945(11) = 13 and (13+31)/2 = 22.
a(12) = 33 because A275945(12) = 15 and (15+51)/2 = 33.

Links

Crossrefs

Cf. A007953, A055642, A273492, A275945.

Programs

A273492 Numbers n such that the average of different permutations of digits of n is not an integer.

Original entry on oeis.org

10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 1000, 1001, 1002, 1004, 1005, 1006, 1008, 1009, 1010, 1011, 1013, 1014, 1015, 1017, 1018, 1019, 1020, 1022, 1023, 1024
Offset: 1

Views

Author

Altug Alkan, Aug 29 2016

Keywords

Comments

Complement of A275945.
Permutations with a first digit of 0 are included in the average (i.e. 0010 is taken to be 10, 01 is taken to be 1, etc.).
From Robert Israel, Sep 01 2016: (Start)
n such that A002275(A055642(n))*A007953(n) is not divisible by A055642(n).
In particular, contains no k-digit numbers if k is in A014950. (End)

Examples

			12 is a term because (12+21) = 33 is not divisible by 2.
1000 is a term because (1+10+100+1000) = 1111 is not divisible by 4.
123 is not a term because (123+132+213+231+312+321) is divisible by 6.
1001 is a term because (11+101+110+1001+1010+1100) is not divisible by 6.

Links

Crossrefs

Cf. A002275, A014950, A055642, A066642, A007953, A045876, A055642, A275945.

Programs

  • Maple
    f:= proc(n) local L,d,s;
  L:= convert(n,base,10);
  d:= nops(L);
  s:= convert(L,`+`);
  evalb(s*(10^d-1)/9 mod d = 0)
end proc:
remove(f, [$1..10000]); # Robert Israel, Sep 01 2016
  • Mathematica
    Select[Range[2^10], ! IntegerQ@ Mean@ Map[FromDigits, Permutations@ #] &@ IntegerDigits@ # &] (* Michael De Vlieger, Aug 29 2016 *)
  • PARI
    A055642(n) = #Str(n);
A007953(n) = sumdigits(n);
for(n=1, 2000, if((((10^A055642(n)-1)/9)*A007953(n)) % A055642(n) != 0, print1(n, ", ")));

A161020 All the non-repdigit terms of A160818.

Original entry on oeis.org

370, 407, 481, 518, 592, 629, 370370, 407407, 481481, 518518, 592592, 629629, 370370370, 407407407, 456790123, 469135802, 481481481, 493827160, 506172839, 518518518, 530864197, 543209876, 592592592, 629629629, 370370370370
Offset: 1

Views

Author

Johan Särnbratt, Jun 02 2009

Keywords

Comments

All known terms are multiples of 111/3 = 37.
Non-repdigit numbers n such that ((10^A055642(n)-1)/9)*(A007953(n)/A055642(n)) = n. So the sequence is infinite. - Altug Alkan, Sep 05 2016

Examples

			For example with 370: (073+037+307+370+703+730)/6 = 370.

Crossrefs

Cf. A160818, A275772, A275945.

Programs

  • Maple
    read("transforms3") ; isrep := proc(n) if nops(convert(convert(n,base,10),set)) = 1 then true; else false; fi; end: a160818 := BFILETOLIST("b160818.txt") ; for i from 1 to 400 do a := op(i,a160818) ; if not isrep(a) then printf("%d,",a) ; fi; od: # R. J. Mathar, Jul 04 2009

Extensions

More terms from R. J. Mathar, Jul 04 2009
Showing 1-3 of 3 results.

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

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