A369274 -id:A369274 - cp's OEIS frontend

A369273 Nonnegative numbers k satisfying sin(k) < sin(k+1) < sin(k+2).

0, 5, 6, 11, 12, 17, 18, 24, 25, 30, 31, 36, 37, 42, 43, 44, 49, 50, 55, 56, 61, 62, 68, 69, 74, 75, 80, 81, 86, 87, 88, 93, 94, 99, 100, 105, 106, 112, 113, 118, 119, 124, 125, 130, 131, 132, 137, 138, 143, 144, 149, 150, 156, 157, 162, 163, 168, 169, 174, 175, 181, 182, 187, 188, 193, 194

Offset: 1

R. J. Mathar, Jan 18 2024

Subsequence of terms in A026309: The smaller of two consecutive terms there.

The terms A246389(.)-2 almost match the terms here; the exceptions are terms 178, 220, 266, 310, 555, 599, ... in A246389 where the associates 176, 218, 264, 308, ... are not in this sequence. - Hugo Pfoertner, Jan 18 2024

Cf. A026309, A369274, A369275.

isA369273 := proc(k)
    local s ;
    s := [seq(evalf(sin(k+i)),i=0..2)] ;
    if s[1] < s[2] and s[2] < s[3] then
        true;
    else
        false;
    end if;
end proc:
A369273 := proc(n)
    option remember ;
    if n = 1 then
        0;
    else
        for a from procname(n-1)+1 do
            if isA369273(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A369273(n),n=1..100) ;

Select[Range[0,194], Sin[#]James C. McMahon, Jan 22 2024 *)

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

Original entry on oeis.org

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

R. J. Mathar, Jan 18 2024

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
Both patterns break. The first at n = 7035 and the second at n = 7019. In general this sequence is not periodic mod m for m > 1 as the (period of sin(x))/(1) is irrational. - David A. Corneth, Dec 10 2024
Mathar’s conjecture is true: these are just the numbers which are between Pi*3/2 - 1/2 and Pi*5/2 - 7/2 mod 2*Pi, and reducing the upper bound by 1 leaves it empty. - Charles R Greathouse IV, Dec 10 2024

David A. Corneth, Table of n, a(n) for n = 1..10000

Subsequence of A369274 and hence of A369273 and A026309.

Cf. A096444.

Select[Range[0,2350], Sin[#]James C. McMahon, Jan 20 2024 *)
Flatten[Position[Partition[Sin[Range[2500]],5,1],?(Min[Differences[#]]>0&)]]//Quiet (* _Harvey P. Dale, Dec 10 2024 *)

first(n) = {
	my(res = List(), streak = 1, s = sin(1));
	for(i = 2, oo,
		c = sin(i);
		if(c > s,
			streak++;
			if(streak >= 5,
				listput(res, i-4);
				if(#res >= n,
					return(res)));
		,
			streak = 1);
s = c); res} \\ David A. Corneth, Dec 11 2024

a(n) ~ k*n where k = 2*Pi/(Pi - 3) = 44.375... by the Equidistribution Theorem. - Charles R Greathouse IV, Dec 10 2024

cp's OEIS Frontend

A369273 Nonnegative numbers k satisfying sin(k) < sin(k+1) < sin(k+2).

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