This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345922 #6 Jul 12 2021 18:01:59
%S A345922 2,11,12,14,37,40,42,47,51,52,54,59,60,62,137,144,146,151,157,163,164,
%T A345922 166,171,172,174,181,184,186,191,197,200,202,207,211,212,214,219,220,
%U A345922 222,229,232,234,239,243,244,246,251,252,254,529,544,546,551,557,569
%N A345922 Numbers k such that the k-th composition in standard order (row k of A066099) has reverse-alternating sum 2.
%C A345922 The reverse-alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(k-i) y_i.
%C A345922 The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
%e A345922 The initial terms and the corresponding compositions:
%e A345922 2: (2) 144: (3,5)
%e A345922 11: (2,1,1) 146: (3,3,2)
%e A345922 12: (1,3) 151: (3,2,1,1,1)
%e A345922 14: (1,1,2) 157: (3,1,1,2,1)
%e A345922 37: (3,2,1) 163: (2,4,1,1)
%e A345922 40: (2,4) 164: (2,3,3)
%e A345922 42: (2,2,2) 166: (2,3,1,2)
%e A345922 47: (2,1,1,1,1) 171: (2,2,2,1,1)
%e A345922 51: (1,3,1,1) 172: (2,2,1,3)
%e A345922 52: (1,2,3) 174: (2,2,1,1,2)
%e A345922 54: (1,2,1,2) 181: (2,1,2,2,1)
%e A345922 59: (1,1,2,1,1) 184: (2,1,1,4)
%e A345922 60: (1,1,1,3) 186: (2,1,1,2,2)
%e A345922 62: (1,1,1,1,2) 191: (2,1,1,1,1,1,1)
%e A345922 137: (4,3,1) 197: (1,4,2,1)
%t A345922 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A345922 sats[y_]:=Sum[(-1)^(i-Length[y])*y[[i]],{i,Length[y]}];
%t A345922 Select[Range[0,100],sats[stc[#]]==2&]
%Y A345922 These compositions are counted by A088218.
%Y A345922 The case of partitions is counted by A120452.
%Y A345922 These are the positions of 2's in A344618.
%Y A345922 The opposite (negative 2) version is A345923.
%Y A345922 The version for unreversed alternating sum is A345925.
%Y A345922 The version for Heinz numbers of partitions is A345961.
%Y A345922 A000041 counts partitions of 2n with alternating sum 0, ranked by A000290.
%Y A345922 A011782 counts compositions.
%Y A345922 A097805 counts compositions by alternating (or reverse-alternating) sum.
%Y A345922 A103919 counts partitions by sum and alternating sum (reverse: A344612).
%Y A345922 A316524 gives the alternating sum of prime indices (reverse: A344616).
%Y A345922 A344610 counts partitions by sum and positive reverse-alternating sum.
%Y A345922 A344611 counts partitions of 2n with reverse-alternating sum >= 0.
%Y A345922 A345197 counts compositions by sum, length, and alternating sum.
%Y A345922 Standard compositions: A000120, A066099, A070939, A228351, A124754, A344618.
%Y A345922 Compositions of n, 2n, or 2n+1 with alternating/reverse-alternating sum k:
%Y A345922 - k = 0: counted by A088218, ranked by A344619/A344619.
%Y A345922 - k = 1: counted by A000984, ranked by A345909/A345911.
%Y A345922 - k = -1: counted by A001791, ranked by A345910/A345912.
%Y A345922 - k = 2: counted by A088218, ranked by A345925/A345922.
%Y A345922 - k = -2: counted by A002054, ranked by A345924/A345923.
%Y A345922 - k >= 0: counted by A116406, ranked by A345913/A345914.
%Y A345922 - k <= 0: counted by A058622(n-1), ranked by A345915/A345916.
%Y A345922 - k > 0: counted by A027306, ranked by A345917/A345918.
%Y A345922 - k < 0: counted by A294175, ranked by A345919/A345920.
%Y A345922 - k != 0: counted by A058622, ranked by A345921/A345921.
%Y A345922 - k even: counted by A081294, ranked by A053754/A053754.
%Y A345922 - k odd: counted by A000302, ranked by A053738/A053738.
%Y A345922 Cf. A000070, A000097, A025047, A027193, A034871, A114121, A163493, A236913, A344607, A344608, A344741, A344743.
%K A345922 nonn
%O A345922 1,1
%A A345922 _Gus Wiseman_, Jul 10 2021