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 1-4 of 4 results.

A181182 Primes in A181178.

Original entry on oeis.org

11, 31, 41, 61, 71, 137, 193, 257, 467, 1399, 2887, 35999, 599699, 4987999, 589998989, 2899889999, 58989999989, 58799999999999, 579999998999999, 19999999999997999, 199999999999898999, 499999999999899989, 699999999999979999, 799999999999988999, 4999999999998899999, 7999999999998999899, 79999999999988999999
Offset: 1

Views

Author

Jonathan Vos Post, Jan 25 2011

Keywords

Examples

			a(2) = 31 because 31 is prime, and is the 4th (zero-free positive) number with digital sum 4 {4,13,22,31,112,121,211,1111}.
		

Crossrefs

Formula

Intersection of A000040 and A181178.

Extensions

a(13) and a(14) from Zak Seidov, Jan 26 2011
Terms a(15) onward from Max Alekseyev, Aug 19 2013

A081927 n-th positive integer whose digits sum up to n.

Original entry on oeis.org

1, 11, 21, 31, 41, 51, 61, 71, 81, 109, 137, 165, 193, 257, 294, 376, 467, 567, 676, 785, 894, 1399, 1778, 1986, 2887, 3869, 4869, 5878, 6887, 7896, 8959, 9968, 18798, 26998, 35999, 45999, 56899, 66989, 76998, 87799, 97889, 178899, 199798, 298988, 398988
Offset: 1

Views

Author

Amarnath Murthy, Apr 01 2003

Keywords

Examples

			31 is the 4th integer of the sequence and the 4th number whose digits sum up to 4 : 4, 13, 22, [31], 103, 112, 121, 130, ...
109 is the 10th integer of the sequence and the 10th number whose digits sum up to 10 : 19, 28, 37, 46, 55, 64, 73, 82, 91, [109], 118, 127, 136, ...
		

Crossrefs

Leading diagonal of A081926.

Programs

  • Maple
    f:= proc(n) local Res, d, v, count;
        count:= 0;
        for d from ceil(n/9) while count < n do
           v:= g(n,d,n-count,1);
           Res:= v[-1];
           count:= count + nops(v);
        od:
        Res
    end proc:
    g:= proc(n,d,remain) local rem, Res, j, j0, v;
          if remain = 0 then return [] else rem:= remain fi;
          if nargs = 4 then j0:= 1 else j0:= 0 fi;
          if d = 1 then if n >= j0 and n <= 9 then [n] else [] fi
          else
            Res:= NULL;
            for j from max(j0, ceil(n-9*(d-1))) to min(9,n) while rem > 0 do
              v:= map(t -> j*10^(d-1)+t, procname(n-j,d-1,rem));
              Res:= Res, op(v);
              rem:= rem - nops(v);
            od;
            [Res]
          fi
    end proc:
    map(f, [$1..200]); # Robert Israel, Feb 19 2018
  • Mathematica
    Table[Select[Range[500000],Total[IntegerDigits[#]]==n&][[n]],{n,45}] (* Harvey P. Dale, Mar 02 2024 *)

Formula

From Robert Israel, Feb 20 2018: (Start)
a(9*k-j) = (12-j)*10^(k-1) - 10^(k-10) - 10^(j+k-45) - 1 for j=2..9, k >= 45-j.
a(9*k-1) = 2*10^k - 10^(k-9) - 10^(k-35) - 1, k >= 35. (End)

Extensions

Corrected and extended by Ray Chandler, Oct 29 2003

A181321 Primes with digital sum 70.

Original entry on oeis.org

189997999, 199799989, 199898899, 199997899, 199997989, 199998889, 268999999, 269998999, 278989999, 278999989, 279889999, 279988999, 287998999, 287999989, 288998989, 288999889, 288999979, 289699999, 289789999, 289889989
Offset: 1

Views

Author

Zak Seidov, Jan 26 2011

Keywords

Comments

The sequence begins with 8438 9-digit numbers.
Then there are 739572 10-digit numbers.
All terms == 7 (mod 18).

Crossrefs

Cf. similar sequences listed in A244918.

Programs

  • Magma
    [p: p in PrimesUpTo(3*10^8) | &+Intseq(p) eq 70]; // Vincenzo Librandi, Jul 09 2014
    
  • Mathematica
    Select[Prime[Range[3*10^8]], Total[IntegerDigits[#]]==70 &] (* Vincenzo Librandi, Jul 09 2014 *)
  • Python
    # see code in A107579 which can be used to produce this sequence by giving the initial term p = 189997999 (or 8*10**7-1, for digit sum 70). - M. F. Hasler, Mar 16 2022

A181181 Product of the first n zero-free positive numbers with digital sum n.

Original entry on oeis.org

1, 22, 756, 35464, 2112320, 152681760, 12984899200, 1270453824640, 140587147048320, 204867922610391040, 222308451584243548160, 277934723066170025856000, 385262452280397590195584000, 954777912911324324000159027200, 3057686768847576381964905048883200
Offset: 1

Views

Author

Jonathan Vos Post, Jan 25 2011

Keywords

Comments

Product of the first n values in the n-th row of the triangular array A069800 in which n-th row consists of numbers (excluding the digit 0) with digit sum n arranged in increasing numerical order.

Examples

			a(3) = 756 = 3 * 12 * 21.
a(4) = 35464 = 4 * 13 * 22 * 31.
a(5) = 2112320 = 5 * 14 * 23 * 32 * 41.
		

Crossrefs

Showing 1-4 of 4 results.