A383284 -id:A383284 - cp's OEIS frontend

A265576 LCM-transform of EKG sequence A064413.

1, 2, 2, 3, 1, 3, 1, 2, 5, 1, 1, 1, 7, 1, 1, 1, 2, 1, 11, 1, 1, 3, 1, 5, 1, 1, 13, 1, 1, 1, 2, 17, 1, 1, 1, 19, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 29, 1, 1, 1, 31, 1, 1, 1, 2, 1, 37, 1, 1, 1, 1, 1, 1, 41, 1, 1, 3, 1, 1, 1, 43, 1, 1, 1, 1, 1, 1, 1, 47, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 53

Offset: 1

N. J. A. Sloane, Jan 02 2016

nonn

This is not equal to A383293(n) = A014963(A064413(n)) because the EKG-permutation doesn't satisfy the property that all prime powers should appear before any of their multiples, as, for example, A064413(4) = 6 comes before A064413(5) = 3. See comments in A368900. - Antti Karttunen, Jan 13 2024

Antti Karttunen, Table of n, a(n) for n = 1..20000
Andrzej Nowicki, Strong divisibility and LCM-sequences, arXiv:1310.2416 [math.NT], 2013.
Andrzej Nowicki, Strong divisibility and LCM-sequences, Am. Math. Mnthly 122 (2015), 958-966.
Index entries for sequences related to EKG sequence.

Cf. A064413, A383284 (rgs-transform), A383285 (positions of terms > 1), A383295.
Positions of records: {2} U A064423.
Other LCM-transforms are A014963, A061446, A265574, A265575, A368900 (see the last one for many other examples), A383258.
Cf. also A383293.

LCMXfm:=proc(a) local L,i,n,g,b;
L:=nops(a);
g:=Array(1..L,0); b:=Array(1..L,0);
b[1]:=a[1]; g[1]:=a[1];
for n from 2 to L do g[n]:=ilcm(g[n-1],a[n]); b[n]:=g[n]/g[n-1]; od;
lprint([seq(b[i],i=1..L)]);
end;
# let t1 contain the first 100 terms of A064413
LCMXfm(t1);

LCMXfm[a_List] := Module[{L = Length[a], b, g}, b[1] = g[1] = a[[1]]; b[] = 0; g[] = 0; Do[g[n] = LCM[g[n - 1], a[[n]]]; b[n] = g[n]/g[n - 1], {n, 2, L}]; Array[b, L]];
ekg[1] = 1; ekg[2] = 2; ekg[n_] := ekg[n] = For[k = 1, True, k++, If[FreeQ[ Array[ekg, n - 1], k] && !CoprimeQ[k, ekg[n - 1]], Return[k]]];
LCMXfm[Array[ekg, 100]] (* Jean-François Alcover, Dec 05 2017 *)

LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2, len, g[n] = lcm(g[n-1], v[n]); b[n] = g[n]/g[n-1]); (b); };
up_to = 20000;
v265576 = LCMtransform(vector(up_to, i, A064413(i))); \\ With precomputed A064413.
A265576(n) = v265576[n]; \\ Antti Karttunen, Apr 21 2025

a(n) = lcm {1..A064413(n)} / lcm {1..A064413(n-1)}. - Antti Karttunen, Apr 21 2025

More terms from Antti Karttunen, Apr 21 2025

A383285 Positions of terms > 1 in A265576, where A265576 is the LCM-transform of EKG-sequence.

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 13, 17, 19, 22, 24, 27, 31, 32, 36, 42, 50, 56, 60, 64, 66, 73, 76, 80, 88, 99, 106, 112, 114, 122, 124, 127, 133, 137, 150, 159, 166, 171, 181, 188, 196, 202, 206, 215, 232, 235, 240, 252, 258, 263, 278, 286, 290, 296, 304, 313, 319, 327, 335, 343, 359, 362, 370, 376, 380, 400, 419, 429, 437, 443

Offset: 1

Antti Karttunen, Apr 22 2025

nonn

Antti Karttunen, Table of n, a(n) for n = 1..22747
Index entries for sequences related to EKG sequence.

Positions of terms larger than one in A265576 and in A383284.
Cf. A064413.
Cf. A064423 (after its initial 1 is a subsequence of this sequence), A383295 (conjectured subsequence).

cp's OEIS Frontend

A265576 LCM-transform of EKG sequence A064413.

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