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%I #25 Feb 20 2024 10:32:50
%S 42,86,130,199,243,287,331,375,419,463,507,532,576,620,664,708,752,
%T 796,840,909,953,997,1041,1085,1129,1173,1217,1242,1286,1330,1374,
%U 1418,1462,1506,1550,1619,1663,1707,1751,1795,1839,1883,1927,1952,1996,2040,2084,2128,2172,2216,2260,2329
%N Nonnegative numbers k satisfying sin(k) < sin(k+1) < sin(k+2) < sin(k+3) < sin(k+4).
%C This is a subsequence of terms in A369274: The smaller of two consecutive terms there.
%C 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.
%C 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
%t Select[Range[0,2350], Sin[#]<Sin[#+1]<Sin[#+2]<Sin[#+3]<Sin[#+4]&] (* _James C. McMahon_, Jan 20 2024 *)
%Y Cf. A026309, A369273, A369274.
%K nonn,easy
%O 1,1
%A _R. J. Mathar_, Jan 18 2024
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