A252022 -id:A252022 - cp's OEIS frontend

A252079 Fixed points of permutations A252022 and A252023.

1, 2, 3, 4, 5, 36, 72, 125, 136, 900, 4454, 8021, 27223, 33905, 73222, 127536, 146353, 180177, 234668, 273241

Offset: 1

Reinhard Zumkeller, Dec 13 2014

Cf. A252022, A252023, A252078.

a252079 n = a252079_list !! (n-1)
a252079_list = [x | x <- [1..], a252022 x == x]

A252079_list, l, s, b = [1], [1], 2, set()
for n in range(2, 10**5):
    i = s
    while True:
        if i not in b:
            li = [int(d) for d in str(i)[::-1]]
            for x, y in zip(li, l):
                if x+y > 9:
                    break
            else:
                l = li
                b.add(i)
                if i == n:
                    A252079_list.append(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
        i += 1 # Chai Wah Wu, Dec 14 2014

a(16)-a(20) from Chai Wah Wu, Dec 14 2014

A252023 Inverse permutation to A252022.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 9, 15, 21, 6, 8, 10, 11, 12, 13, 17, 19, 23, 41, 14, 16, 18, 25, 26, 27, 29, 34, 43, 50, 20, 24, 28, 30, 31, 32, 36, 45, 53, 58, 22, 33, 35, 37, 38, 39, 47, 56, 60, 90, 40, 44, 46, 48, 62, 64, 74, 80, 92, 105, 42, 54, 66, 68, 76, 78, 82, 94

Offset: 1

Reinhard Zumkeller, Dec 12 2014

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A252022 (inverse), A252079 (fixed points).

import Data.List (elemIndex); import Data.Maybe (fromJust)
a252023 = (+ 1) . fromJust . (`elemIndex` a252022_list)

A262604 First difference of A252022.

Original entry on oeis.org

1, 1, 1, 1, 5, -4, 5, -4, 5, 1, 1, 1, 5, -12, 13, -5, 6, -5, 13, -21, 31, -22, 13, -8, 1, 1, 7, -6, 7, 1, 1, 6, -14, 15, -6, 7, 1, 1, 5, -31, 41, -32, 23, -14, 15, -6, 7, 47, -71, 41, 31, -63, 23, 41, -55, 63, -71, 81, -72, 63, -57, 49, -48, 49, -42, 43, -42

Offset: 1

Paul Tek, Sep 26 2015

The graph of the sequence exhibits a kind of symmetry around the X-axis.

Paul Tek, Table of n, a(n) for n = 1..20000

Cf. A252022.

a262604 n = a262604_list !! (n-1)
a262604_list = zipWith (-) (tail a252022_list) a252022_list
-- Reinhard Zumkeller, Sep 27 2015

a(n) = A252022(n+1) - A252022(n) for any n>0.

A252001 Lexicographically earliest permutation of the positive integers, such that a carry occurs when adjacent terms are added in decimal representation.

Original entry on oeis.org

1, 9, 2, 8, 3, 7, 4, 6, 5, 15, 16, 14, 17, 13, 18, 12, 19, 11, 29, 21, 39, 22, 28, 23, 27, 24, 26, 25, 35, 36, 34, 37, 33, 38, 32, 48, 42, 49, 31, 59, 41, 60, 40, 61, 43, 47, 44, 46, 45, 55, 50, 51, 52, 53, 54, 56, 57, 58, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset: 1

Reinhard Zumkeller, Dec 12 2014

a(n+1) = smallest number, not occurring earlier, such that a carry occurs when adding it to a(n) in decimal arithmetic.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Carry
Wikipedia, Carry (arithmetic)
Index entries for sequences that are permutations of the natural numbers

Cf. A252022 (no carries); A252002 (inverse), A252078 (fixed points), A251984, A167831.

Cf. A262703 (first differences).

import Data.List (delete)
a252001 n = a252001_list !! (n-1)
a252001_list = 1 : f [1] (drop 2 a031298_tabf) where
   f xs zss = g zss where
     g (ds:dss) = if any (> 9) $ zipWith (+) xs ds
       then (foldr (\d v -> 10 * v + d) 0 ds) : f ds (delete ds zss)
       else g dss

A329804 Lexicographically earliest sequence of distinct positive integers such that the product a(n)*a(n+1) is "doubly true" (see the Comments section).

Original entry on oeis.org

1, 2, 3, 10, 4, 16, 20, 5, 19, 30, 6, 21, 40, 7, 50, 8, 60, 9, 70, 11, 80, 12, 90, 13, 18, 38, 100, 14, 46, 105, 22, 61, 36, 103, 34, 106, 15, 93, 108, 25, 102, 35, 41, 29, 104, 26, 110, 17, 120, 23, 28, 109, 37, 130, 24, 72, 107, 43, 140, 27, 62, 31, 150, 32

Offset: 1

Eric Angelini and Lars Blomberg, Nov 21 2019

A "doubly true" product p*q has the property that the numerical product p*q is r and (the product of the digits of p) times (the product of the digits of q) is equal to the product of the digits of r.
As the sequence can always be extended with an integer ending in zero, it is infinite.
The sequence is a permutation of the positive integers.

			13*18 = 234 and (1*3)*(1*8) = 2*3*4
18*38 = 684 and (1*8)*(3*8) = 6*8*4
38*100 = 3800 and (3*8)*(1*0*0) = 3*8*0*0.

N. J. A. Sloane, Table of n, a(n) for n = 1..35000 (first 10000 terms from Lars Blomberg)
Rémy Sigrist, Scatterplot of the first 100000 terms.
Rémy Sigrist, Scatterplot of (n, a(n)-n) for n = 1..500000.

Cf. A007954, A252022 (same idea, but with doubly true additions).

dp(m) = vecprod(digits(m))
{ s=0; u=v=1; for (n=1, 64, print1 (v", "); s+=2^v; while (bittest(s,u), u++); for (w=u, oo, if (!bittest(s,w) && dp(v)*dp(w)==dp(v*w), v=w; break))) } \\ Rémy Sigrist, Nov 21 2019

Edited by N. J. A. Sloane, Dec 09 2019

A336193 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n + a(n) can be computed without carry in base 10.

Original entry on oeis.org

1, 2, 3, 4, 10, 11, 12, 20, 30, 5, 6, 7, 13, 14, 21, 22, 31, 40, 50, 8, 15, 16, 23, 24, 32, 33, 41, 51, 60, 9, 17, 25, 26, 34, 42, 43, 52, 61, 100, 18, 27, 35, 36, 44, 53, 101, 102, 110, 120, 19, 28, 37, 45, 103, 104, 111, 112, 121, 130, 29, 38, 105, 106, 113

Offset: 1

Rémy Sigrist, Jul 11 2020

This sequence is a decimal variant of A238757.

This sequence is a self-inverse permutation of the natural numbers.

			The first terms, alongside n + a(n), are:
  n   a(n)  n+a(n)
  --  ----  ------
   1     1       2
   2     2       4
   3     3       6
   4     4       8
   5    10      15
   6    11      17
   7    12      19
   8    20      28
   9    30      39
  10     5      15
  11     6      17
  12     7      19
  13    13      26
  14    14      28
  15    21      36

Cf. A007953, A238757, A252022.

s=0; for (n=1, 64, for (v=1, oo, if (!bittest(s,v) && sumdigits(n+v)==sumdigits(n)+sumdigits(v), print1(v", "); s+=2^v; break)))

A007953(n + a(n)) = A007953(n) + A007953(a(n)).

A352877 Lexicographically earliest sequence of distinct nonnegative terms such that two consecutive terms can be added without carries in base 3.

Original entry on oeis.org

0, 1, 3, 2, 6, 9, 4, 10, 7, 18, 5, 12, 11, 15, 27, 8, 36, 13, 28, 16, 37, 30, 14, 39, 29, 21, 31, 19, 33, 20, 54, 17, 63, 81, 22, 55, 24, 56, 84, 23, 57, 82, 25, 108, 26, 135, 83, 42, 38, 87, 45, 32, 48, 85, 40, 90, 34, 46, 88, 64, 91, 43, 109, 49, 111, 41, 93

Offset: 0

Rémy Sigrist, Apr 06 2022

This sequence is a permutation of the positive integers, analogous to A109812 and A252022.

			The first terms, alongside their ternary expansions, are:
  n   a(n)  ter(a(n))
  --  ----  ---------
   0     0          0
   1     1          1
   2     3         10
   3     2          2
   4     6         20
   5     9        100
   6     4         11
   7    10        101
   8     7         21
   9    18        200
  10     5         12
  11    12        110
  12    11        102

Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A109812 (binary analog), A252022 (decimal analog).

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A252079 Fixed points of permutations A252022 and A252023.

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A252023 Inverse permutation to A252022.

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A262604 First difference of A252022.

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A252001 Lexicographically earliest permutation of the positive integers, such that a carry occurs when adjacent terms are added in decimal representation.

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A329804 Lexicographically earliest sequence of distinct positive integers such that the product a(n)*a(n+1) is "doubly true" (see the Comments section).

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A336193 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, n + a(n) can be computed without carry in base 10.

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PARI

Formula

A352877 Lexicographically earliest sequence of distinct nonnegative terms such that two consecutive terms can be added without carries in base 3.

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