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%I #11 Nov 28 2024 21:31:02
%S 1,2,3,6,7,10,11,12,14,15,19,20,21,25,26,28,30,32,33,34,37,38,39,42,
%T 44,45,48,49,50,51,53,54,55,57,58,59,61,62,63,65,66,67,68,72,73,74,75,
%U 77,78,81,82,84,85,86,87,88,96,97,98,100,101,102,104,106,107,108,114,116,117,118,119,120,121,122,123,124,126,127,129,130,131,132,134,135,136,137,140,141,142,143,144,145,148
%N Numbers k such that A073259(k)=4: the length of iteration-transient leading to k-th composite number equals 4.
%H Sean A. Irvine, <a href="/A073439/b073439.txt">Table of n, a(n) for n = 1..4662</a>
%e The sequence is probably finite and given in full. a(1)=1: the fixed point list from m=a(1) to composite[m] is: {1,2,3,4}, the length is 4; largest term seems to be a(4662)=77629, with transient list {77629,85259,85933,85990}. The terms appears in bursts of consecutive integers. A chain of 37 consecutive numbers starts at 28046.
%t lfp[x_] := Length[FixedPointList[x+PrimePi[ # ]+1&, x]]-1 Do[s=lfp[n]; If[Equal[s, 4], Print[n]], {n, 1, 10000000}]
%Y Cf. A002808, A073259, A073320.
%K nonn
%O 1,2
%A _Labos Elemer_, Jul 31 2002
%E Offset corrected by _Sean A. Irvine_, Nov 28 2024