A379015 -id:A379015 - cp's OEIS frontend

A379040 Fixed points in A379015.

0, 1, 5, 9, 13, 17, 21, 33, 45, 57, 65, 73, 85, 93, 129, 165, 173, 189, 205, 217, 241, 257, 273, 297, 309, 325, 341, 381, 441, 513, 585, 645, 685, 733, 765, 797, 845, 857, 889, 921, 945, 993, 1025, 1057, 1105, 1129, 1161, 1193, 1205, 1253, 1285, 1317, 1365, 1389

Offset: 1

Darío Clavijo, Dec 14 2024

Such points exist when the non-adjacent form representation of n is palindromic.

Wikipedia, Non-adjacent form.

Cf. A379015.

def isok(n):
    E, r = n, 0
    while E:
        if E & 1:
            Zi = 2 - (E & 3)
            E -= Zi
            r += Zi
        E >>= 1
        r <<= 1
    return (r >> 1) == n
print([n for n in range(0,1400) if isok(n)])

Leading 0 added by Rémy Sigrist, Dec 28 2024

A377625 Nonnegative numbers whose nonadjacent form is antipalindromic.

Original entry on oeis.org

0, 3, 7, 15, 31, 51, 63, 75, 99, 127, 155, 195, 231, 255, 279, 315, 387, 455, 511, 567, 635, 723, 771, 819, 903, 975, 1023, 1071, 1143, 1227, 1275, 1323, 1427, 1539, 1651, 1799, 1935, 2047, 2159, 2295, 2443, 2555, 2667, 2835, 2979, 3075, 3171, 3315, 3495, 3591

Offset: 1

Rémy Sigrist, Dec 28 2024

Also nonnegative numbers k such that A379015(k) = -k.

			The first terms, alongside their nonadjacent forms, are:
  n   a(n)  naf(a(n))
  --  ----  ----------
   1     0           0
   2     3         10T
   3     7        100T
   4    15       1000T
   5    31      10000T
   6    51     10T010T
   7    63     100000T
   8    75     1010T0T
   9    99    10T0010T
  10   127    1000000T
  11   155    10100T0T
  12   195   10T00010T
  13   231   100T0100T
  14   255   10000000T
  15   279   10010T00T
  16   315   101000T0T

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Joerg Arndt, Matters Computational (The Fxtbook), pages 61-62.
Wikipedia, Non-adjacent form

See A233571 for a similar sequence.

Cf. A379015, A379040.

is(n) = { my (m = 0, d, r = n); while (r, m *= 2; if (r % 2, r -= d = 2 - (r % 4); m += d;); r \= 2;); m == -n; }

A377477 Consider the nonadjacent form for n, then reverse the digits, leaving any trailing zeros alone, and take the absolute value.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 12, 13, 14, 15, 16, 17, 18, 11, 20, 21, 38, 35, 24, 29, 26, 39, 28, 25, 30, 31, 32, 33, 34, 23, 36, 41, 22, 27, 40, 37, 42, 83, 76, 45, 70, 67, 48, 61, 58, 51, 52, 77, 78, 71, 56, 57, 50, 79, 60, 49, 62, 63, 64, 65, 66, 47

Offset: 0

Rémy Sigrist, Dec 28 2024

A self-inverse permutation of the nonnegative integers.

			For n = 22: the nonadjacent form for 22 is "10T0T0" (where T denotes -1), reversing the digits and leaving any trailing zeros alone yields "T0T010", so a(22) = |- 2^5 - 2^3 + 2^1| =  38.

Rémy Sigrist, Table of n, a(n) for n = 0..10921
Joerg Arndt, Matters Computational (The Fxtbook), pages 61-62.
Rémy Sigrist, PARI program
Wikipedia, Non-adjacent form
Index entries for sequences that are permutations of the natural numbers

See A160652 and A345201 for similar sequences.

Cf. A057889, A184617, A379015.

PARI
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\\ See Links section.
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A184617(a(n)) = A057889(A184617(n)).

cp's OEIS Frontend

A379040 Fixed points in A379015.

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A377625 Nonnegative numbers whose nonadjacent form is antipalindromic.

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A377477 Consider the nonadjacent form for n, then reverse the digits, leaving any trailing zeros alone, and take the absolute value.

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