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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.

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A283192 Lexicographically earliest sequence of distinct terms such that the derived sequence s(n)=CarrylessSum{k=1..n}a(k) contains only distinct terms, where CarrylessSum is the analog of summation for carryless addition.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 9, 10, 8, 11, 12, 13, 14, 15, 16, 17, 18, 20, 19, 22, 21, 23, 28, 24, 25, 26, 29, 30, 27, 31, 32, 33, 35, 34, 36, 38, 37, 41, 40, 39, 42, 44, 52, 45, 43, 46, 47, 54, 48, 51, 55, 56, 49, 67, 62, 50, 53, 61, 58, 57, 63, 64, 71, 59, 66, 65
Offset: 1

Views

Author

Rémy Sigrist, Mar 02 2017

Keywords

Comments

This sequence is a permutation of the natural numbers (with inverse A283194 and fixed points A283206):
- for any k>0, 10^(k-1) is the first k-digit number appearing in this sequence, and the corresponding partial carryless sum is also the first k-digit number appearing in A283193,
- all powers of 10 appear in this sequence, in increasing order,
- if a(m)=10^k, and the least value not yet seen in this sequence, say v, is smaller than 10^k, then a(m+1)=v,
- hence each natural number will eventually appear in this sequence.

Links

Crossrefs

Cf. A169890, A283193 (Partial carryless sum), A283194 (Inverse), A283206 (Fixed points).

A323394 Carryless sum of divisors of n.

Original entry on oeis.org

1, 3, 4, 7, 6, 2, 8, 5, 3, 18, 12, 18, 14, 14, 14, 11, 18, 19, 10, 32, 22, 36, 24, 30, 21, 32, 20, 36, 20, 52, 32, 43, 48, 44, 38, 51, 38, 40, 46, 70, 42, 76, 44, 74, 58, 62, 48, 84, 47, 83, 62, 88, 54, 80, 62, 80, 60, 70, 50, 48, 62, 96, 84, 7, 74, 24, 68, 6
Offset: 1

Views

Author

Rémy Sigrist, Jan 13 2019

Keywords

Comments

This sequence is a variant of A178910 for the base 10.

Examples

			For n = 42:
- the divisors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42,
- the sum of the units is: 1 + 2 + 3 + 6 + 7 + 4 + 1 + 2 = 26 == 6 (mod 10),
- the sum of the tens is: 1 + 2 + 4 = 7,
- hence a(42) = 76.
For n = 973:
- the divisors of 973 are: 1, 7, 139, 973,
- the sum of the units is: 1 + 7 + 9 + 3 = 20 == 0 (mod 10),
- the sum of the tens is: 3 + 7 = 10 == 0 (mod 10),
- the sum of the hundreds is: 1 + 9 = 10 == 0 (mod 10),
- hence a(973) = 0.

Links

Crossrefs

Cf. A000203, A169890, A178910, A323414 (positions of zeros), A323415 (fixed points).

Programs

  • Maple
    f:= proc(n) local t,d,dd,m,i;
t:= Vector(convert(n,base,10));
for d in numtheory:-divisors(n) minus {n} do
  dd:= convert(d,base,10);
  m:= nops(dd);
  t[1..m]:= t[1..m] + Vector(dd) mod 10;
od:
add(t[i]*10^(i-1),i=1..ilog10(n)+1)
end proc:
map(f, [$1..100]); # Robert Israel, Jan 15 2019
  • PARI
    a(n, base=10) = my (v=[]); fordiv (n, d, my (w=Vecrev(digits(d, base))); v=vector(max(#v, #w), k, (if (k>#v, w[k], k>#w, v[k], (v[k]+w[k])%base)))); fromdigits(Vecrev(v), base)

Formula

a(n) <= A000203(n).

A283193 a(n) = CarrylessSum{k=1..n} A283192(k), where CarrylessSum is the analog of summation for carryless addition.

Original entry on oeis.org

1, 3, 6, 0, 5, 2, 8, 7, 17, 15, 26, 38, 41, 55, 60, 76, 83, 91, 11, 20, 42, 63, 86, 4, 28, 43, 69, 88, 18, 35, 66, 98, 21, 56, 80, 16, 44, 71, 12, 52, 81, 23, 67, 19, 54, 97, 33, 70, 24, 62, 13, 68, 14, 53, 10, 72, 22, 75, 36, 84, 31, 94, 58, 29, 78, 34, 99
Offset: 1

Views

Author

Rémy Sigrist, Mar 02 2017

Keywords

Links

Crossrefs

Cf. A169890, A283192.
Showing 1-3 of 3 results.

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

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