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%I #7 Apr 24 2024 13:58:36
%S 1,1,9,1,7,17,1,11,13,25,1,17,5,19,33,1,13,1,29,25,41,1,5,1,11,19,31,
%T 49,1,1,1,17,29,47,37,57,1,1,1,13,11,71,7,43,65,1,1,1,5,17,107,11,65,
%U 49,73,1,1,1,1,13,161,17,49,37,55,81,1,1,1,1,5,121,13,37,7,83,61,89,1,1,1,1,1,91,5,7,11,125,23,67,97
%N Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(1, k) = 8*k-7, and A(n+1, k) = R(A(n, k)), n,k >= 1, where Reduced Collatz function R(n) gives the odd part of 3n+1.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e Array begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
%e ---+------------------------------------------------------------------------
%e 1 | 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 113, 121,
%e 2 | 1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91,
%e 3 | 1, 11, 5, 29, 19, 47, 7, 65, 37, 83, 23, 101, 55, 119, 1, 137,
%e 4 | 1, 17, 1, 11, 29, 71, 11, 49, 7, 125, 35, 19, 83, 179, 1, 103,
%e 5 | 1, 13, 1, 17, 11, 107, 17, 37, 11, 47, 53, 29, 125, 269, 1, 155,
%e 6 | 1, 5, 1, 13, 17, 161, 13, 7, 17, 71, 5, 11, 47, 101, 1, 233,
%e 7 | 1, 1, 1, 5, 13, 121, 5, 11, 13, 107, 1, 17, 71, 19, 1, 175,
%e 8 | 1, 1, 1, 1, 5, 91, 1, 17, 5, 161, 1, 13, 107, 29, 1, 263,
%e 9 | 1, 1, 1, 1, 1, 137, 1, 13, 1, 121, 1, 5, 161, 11, 1, 395,
%e 10 | 1, 1, 1, 1, 1, 103, 1, 5, 1, 91, 1, 1, 121, 17, 1, 593,
%e 11 | 1, 1, 1, 1, 1, 155, 1, 1, 1, 137, 1, 1, 91, 13, 1, 445,
%e 12 | 1, 1, 1, 1, 1, 233, 1, 1, 1, 103, 1, 1, 137, 5, 1, 167,
%e 13 | 1, 1, 1, 1, 1, 175, 1, 1, 1, 155, 1, 1, 103, 1, 1, 251,
%e 14 | 1, 1, 1, 1, 1, 263, 1, 1, 1, 233, 1, 1, 155, 1, 1, 377,
%e 15 | 1, 1, 1, 1, 1, 395, 1, 1, 1, 175, 1, 1, 233, 1, 1, 283,
%e 16 | 1, 1, 1, 1, 1, 593, 1, 1, 1, 263, 1, 1, 175, 1, 1, 425,
%o (PARI)
%o up_to = 91;
%o R(n) = { n = 1+3*n; n>>valuation(n, 2); };
%o A371095sq(n,k) = if(1==n,8*k-7,R(A371095sq(n-1,k)));
%o A371095list(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] = A371095sq((a-(col-1)),col))); (v); };
%o v371095 = A371095list(up_to);
%o A371095(n) = v371095[n];
%Y Cf. A017077 (row 1), A016921 (row 2), A075677.
%Y Cf. also A371096, A371097.
%K nonn,tabl,easy,new
%O 1,3
%A _Antti Karttunen_, Apr 24 2024
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