A353035 -id:A353035 - cp's OEIS frontend

A353036 Records in A119435.

1, 2, 5, 9, 13, 17, 23, 29, 33, 43, 51, 53, 61, 65, 83, 95, 107, 113, 125, 129, 163, 183, 199, 203, 219, 233, 237, 253, 257, 323, 359, 383, 407, 419, 443, 449, 473, 485, 509, 513, 643, 711, 751, 783, 791, 823, 851, 859, 891, 913, 921, 953, 981, 989, 1021, 1025

Offset: 1

Michael De Vlieger, Apr 18 2022

Terms are odd except for a(2) = 2.
(2^k - 1) +- 2 are terms in this sequence for k > 1.
Let S = A119435. S(2^k + 1) = S(2^k - 1) + 4, while S(2^k) is a local minimum in S.
S(2^k - 1) = 2^(k+1) - 3 and S(2^k + 1) = 2^(k+1) + 1.

Michael De Vlieger, Table of n, a(n) for n = 1..1360
Michael De Vlieger, Bitmap of a(n), n = 1..967, vertical exaggeration 12X.
Michael De Vlieger, Binary expansion of a(n), n = 1..967.

Cf. A030101, A119435, A353035, A353037.

a = {1}; nn = 514; r = 0; Do[AppendTo[a, Complement[Range[i + 2 nn], a][[IntegerReverse[i, 2]] ]], {i, 2, nn}]; Reap[Do[If[# > r, r = #; Sow[r]] &@ a[[i]], {i, Length[a]}]][[-1, -1]]

A353037 Positions of records in A119435.

Original entry on oeis.org

1, 2, 3, 5, 7, 9, 11, 15, 17, 19, 23, 27, 31, 33, 35, 39, 47, 55, 63, 65, 67, 71, 79, 87, 95, 111, 119, 127, 129, 131, 135, 143, 159, 175, 191, 207, 223, 239, 255, 257, 259, 263, 271, 287, 303, 319, 351, 367, 383, 415, 431, 447, 479, 495, 511, 513, 515, 519, 527

Offset: 1

Michael De Vlieger, Apr 18 2022

Let S = A119435. S(2^k +- 1) with k > 0 are records in S and thus (2^k - 1) and (2^k + 1) appear in this sequence.

S(2^k - 1) = 2^(k+1) - 3 and S(2^k + 1) = 2^(k+1) + 1, while S(2^k) is a local minimum.

Michael De Vlieger, Table of n, a(n) for n = 1..1360
Michael De Vlieger, Bitmap of a(n), n = 1..967, vertical exaggeration 12X.
Michael De Vlieger, Binary expansion of a(n), n = 1..967.

Cf. A030101, A119435, A353035, A353036.

a = {1}; nn = 527; r = 0; Do[AppendTo[a, Complement[Range[i + 2 nn], a][[IntegerReverse[i, 2]] ]], {i, 2, nn}]; Reap[Do[If[# > r, r = #; Sow[i]] &@ a[[i]], {i, Length[a]}]][[-1, -1]]

cp's OEIS Frontend

A353036 Records in A119435.

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