A069800 -id:A069800 - cp's OEIS frontend

A181178 n-th zerofree positive number with digital sum n.

1, 11, 21, 31, 41, 51, 61, 71, 81, 118, 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

Offset: 1

Jonathan Vos Post, Jan 25 2011

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

For n > 376, a(n) has decimal representation xyy...y, where x = (n+1) mod 9 + 1, and among y's exactly two equal 8 and the rest equal 9. For example, a(377) = 1999999998999999999999999999999999989999999. - Max Alekseyev, Aug 20 2013

			a(1) = 1 because 1 is the 1st number with digital sum 1;
a(2) = 11 because 11 is the 2nd number with digital sum 2 {2,11};
a(3) = 21 because 21 is the 3rd (zerofree positive) number with digital sum 3 {3,12,21,111};
a(4) = 31 because 31 is the 4th (zerofree positive) number with digital sum 4 {4,13,22,31,112,121,211,1111}.

Zak Seidov, Table of n, a(n) for n = 1..70

Cf. A007953, A052382, A069800, A081927.

nn=50; c=Table[0,{nn}]; t=c; cnt=0; n=0; While[cnt

A069801 Triangular array in which the n-th row consists of numbers with digit product n arranged in increasing numerical order; row consists of 0 if no such numbers exist.

Original entry on oeis.org

1, 2, 3, 4, 22, 5, 6, 23, 32, 7, 8, 24, 42, 222, 9, 33, 25, 52, 0, 26, 34, 43, 62, 223, 232, 322, 0, 27, 72, 35, 53, 28, 44, 82, 224, 242, 422, 2222, 0, 29, 36, 63, 92, 233, 323, 332, 0, 45, 54, 225, 252, 522, 37, 73, 0, 0, 38, 46, 64, 83, 226, 234, 243, 262

Offset: 1

Amarnath Murthy, Apr 13 2002

1 is not allowed as a digit, except in the first row.

If n has any prime factor other than 2,3,5 or 7 then a(n) = 0.

			Triangular array begins:
1;
2;
3;
4,  22;
5;
6,  23, 32;
7;
8,  24, 42, 222;
9,  33;
25, 52;
0;
26, 34, 43,  62, 223, 232, 322;

Alois P. Heinz, Rows n = 1..1000, flattened

Cf. A069800.

Corrected and extended by Alois P. Heinz, Sep 24 2013

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

Jonathan Vos Post, Jan 25 2011

			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}.

Max Alekseyev, Table of n, a(n) for n = 1..50

Cf. A000040, A007953, A069800, A181178

Intersection of A000040 and A181178.

a(13) and a(14) from Zak Seidov, Jan 26 2011

Terms a(15) onward from Max Alekseyev, Aug 19 2013

A275536 Differences of the exponents of the adjacent distinct powers of 2 in the binary representation of n (with -1 subtracted from the least exponent present) are concatenated as decimal digits in reverse order.

Original entry on oeis.org

1, 2, 11, 3, 12, 21, 111, 4, 13, 22, 112, 31, 121, 211, 1111, 5, 14, 23, 113, 32, 122, 212, 1112, 41, 131, 221, 1121, 311, 1211, 2111, 11111, 6, 15, 24, 114, 33, 123, 213, 1113, 42, 132, 222, 1122, 312, 1212, 2112, 11112

Offset: 1

Armands Strazds, Aug 01 2016

A preferable representation is a sequence of arrays, since multi-digit items are possible: [1],[2],[1,1],[3],[1,2],[2,1],[1,1,1],[4],[1,3],[2,2],[1,1,2],[3,1],[1,2,1],[2,1,1],[1,1,1,1],[5],[1,4],[2,3],[1,1,3],[3,2],[1,2,2],[2,1,2],[1,1,1,2],[4,1],[1,3,1],[2,2,1],[1,1,2,1],[3,1,1],[1,2,1,1],[2,1,1,1],[1,1,1,1,1],[6],[1,5],[2,4],[1,1,4],[3,3],[1,2,3],[2,1,3],[1,1,1,3],[4,2],[1,3,2],[2,2,2],[1,1,2,2],[3,1,2],[1,2,1,2],[2,1,1,2],[1,1,1,1,2]. 0 is not allowed as a digit.
a(512) is the first term which cannot be expressed unambiguously in decimal. - Charles R Greathouse IV, Aug 02 2016
The first two terms which are equal (because of the ambiguity inherent in using decimal, or more generally any finite base) are a(3) = a(1024) = 11. a(3) corresponds to the array [1,1] while a(1024) corresponds to [11]. - Charles R Greathouse IV, Mar 19 2017

			5 = 2^2 + 2^0, so the representation is [2-0, 0-(-1)] = [2, 1] so a(5) = 12.
6 = 2^2 + 2^1, so the representation is [2-1, 1-(-1)] = [1, 2] so a(6) = 21.
18 = 2^4 + 2^1, so the representation is [4-1, 1-(-1)] = [3, 2] so a(18) = 23.

Charles R Greathouse IV, Table of n, a(n) for n = 1..511

Cf. A069800, A261300, A248646, A256494, A258055, A004086, A004719, A071160.

a(n)=my(v=List(),k); while(n, k=valuation(n,2)+1; n>>=k; listput(v,k)); fromdigits(Vec(v)) \\ Charles R Greathouse IV, Aug 02 2016

function dec2delta($k) {
  $p = -1;
  while ($k > 0) {
    $k -= $c = pow(2, floor(log($k, 2)));
    if ($p > -1) $d[] = $p - floor(log($c, 2));
    $p = floor(log($c, 2));
  }
  $d[] = $p + 1;
  return array_reverse($d);
}
function delta2dec($d) {
  $k = 0;
  $e = -1;
  foreach ($d AS $v) {
    if ($v > 0) {
      $e += $v;
      $k += pow(2, $e);
    }
  }
  return $k;
}

For n=1..511, a(n) = A004086(A004719(A071160(n))) [In other words, terms of A071160 with 0-digits deleted and the remaining digits reversed.] - Antti Karttunen, Sep 03 2016

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

Jonathan Vos Post, Jan 25 2011

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.

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

Cf. A007953, A069800, A181178.

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A181178 n-th zerofree positive number with digital sum n.

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A069801 Triangular array in which the n-th row consists of numbers with digit product n arranged in increasing numerical order; row consists of 0 if no such numbers exist.

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A181182 Primes in A181178.

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A275536 Differences of the exponents of the adjacent distinct powers of 2 in the binary representation of n (with -1 subtracted from the least exponent present) are concatenated as decimal digits in reverse order.

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

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