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A372282 Array read by upward antidiagonals: A(n, k) = A371094(A(n-1, k)) for n > 1, k >= 1; A(1, k) = 2*k-1.

%I A372282 #22 May 06 2024 08:44:55
%S A372282 1,21,3,5461,21,5,357913941,5461,341,7,1537228672809129301,357913941,
%T A372282 1398101,45,9,28356863910078205288614550619314017621,
%U A372282 1537228672809129301,23456248059221,1109,117,11,9649340769776349618630915417390658987772498722136713669954798667326094136661,28356863910078205288614550619314017621,6602346876188694799461995861,873813,11605,69,13
%N A372282 Array read by upward antidiagonals: A(n, k) = A371094(A(n-1, k)) for n > 1, k >= 1; A(1, k) = 2*k-1.
%e A372282 Array begins:
%e A372282 n\k|    1     2        3     4      5     6        7     8      9     10
%e A372282 ---+----------------------------------------------------------------------
%e A372282 1  |    1,    3,       5,    7,     9,   11,      13,   15,    17,    19,
%e A372282 2  |   21,   21,     341,   45,   117,   69,     341,   93,   213,   117,
%e A372282 3  | 5461, 5461, 1398101, 1109, 11605, 3413, 1398101, 2261, 87381, 11605,
%o A372282 (PARI)
%o A372282 up_to = 28;
%o A372282 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372282 A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
%o A372282 A372282list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A372282sq((a-(col-1)),col))); (v); };
%o A372282 v372282 = A372282list(up_to);
%o A372282 A372282(n) = v372282[n];
%Y A372282 Cf. A005408 (row 1), A372351 (row 2, bisection of A371094), A372444 (column 14).
%Y A372282 Arrays derived from this one:
%Y A372282   A372283,
%Y A372282   A372285 the number of terms of A086893 in the interval [A(n, k), A(1+n, k)],
%Y A372282   A372287 the column index of A(n, k) in array A257852,
%Y A372282   A372288 the sum of digits of A(n, k) in "Jacobsthal greedy base",
%Y A372282   A372353 differences between A(n,k) and the largest term of A086893 <= A(n,k),
%Y A372282   A372354 floor(log_2(.)) of terms, A372356 (and their columnwise first differences),
%Y A372282   A372359 terms xored with binary words of the same length, either of the form 10101...0101 or 110101...0101, depending on whether the binary length is odd or even.
%Y A372282 Cf. also arrays A371096, A371102 that give subsets of columns of this array, and array A371100 that gives the terms of the row 2 in different order.
%K A372282 nonn,tabl,easy
%O A372282 1,2
%A A372282 _Antti Karttunen_, Apr 28 2024