A369275 Nonnegative numbers k satisfying sin(k) < sin(k+1) < sin(k+2) < sin(k+3) < sin(k+4).

42, 86, 130, 199, 243, 287, 331, 375, 419, 463, 507, 532, 576, 620, 664, 708, 752, 796, 840, 909, 953, 997, 1041, 1085, 1129, 1173, 1217, 1242, 1286, 1330, 1374, 1418, 1462, 1506, 1550, 1619, 1663, 1707, 1751, 1795, 1839, 1883, 1927, 1952, 1996, 2040, 2084, 2128, 2172, 2216, 2260, 2329

Offset

1,1

Comments

This is a subsequence of terms in A369274: The smaller of two consecutive terms there.

Conjecture: there is no followup sequence with sin(k) < sin(k+1) < ... < sin(k+5), i.e., there are no two consecutive integers in this sequence.

It appears that, starting at n=4, a(n) mod 2 has a period of 16 with a periodic part consisting of 8 ones followed by 8 zeros. Similarly, starting at n=4, a(n) mod 4 has a period of 32 with a periodic part consisting of 8 threes followed by 8 zeros followed by 8 ones followed by 8 twos. Tested to 5688 terms. - Gary Detlefs, Jan 20 2024

Links

Table of n, a(n) for n=1..52.

Mathematica

Select[Range[0, 2350], Sin[#]<Sin[#+1]<Sin[#+2]<Sin[#+3]<Sin[#+4]&] (* James C. McMahon, Jan 20 2024 *)

Crossrefs

Cf. A026309, A369273, A369274.

Sequence in context: A352481 A019283 A331365 * A300603 A301328 A370521

Adjacent sequences: A369272 A369273 A369274 * A369276 A369277 A369278

Keyword

nonn,easy

Author

R. J. Mathar, Jan 18 2024

Status

approved