cp's OEIS Frontend

A347769 a(0) = 0; a(1) = 1; for n > 1, a(n) = A001065(a(n-1)) = sigma(a(n-1)) - a(n-1) (the sum of aliquot parts of a(n-1)) if this is not yet in the sequence; otherwise a(n) is the smallest number missing from the sequence.

%I A347769 #43 Sep 23 2021 08:03:29
%S A347769 0,1,2,3,4,5,6,7,8,9,10,11,12,16,15,13,14,17,18,21,19,20,22,23,24,36,
%T A347769 55,25,26,27,28,29,30,42,54,66,78,90,144,259,45,33,31,32,34,35,37,38,
%U A347769 39,40,50,43,41,44,46,47,48,76,64,63,49,51,52,53,56,57,58,59,60,108,172
%N A347769 a(0) = 0; a(1) = 1; for n > 1, a(n) = A001065(a(n-1)) = sigma(a(n-1)) - a(n-1) (the sum of aliquot parts of a(n-1)) if this is not yet in the sequence; otherwise a(n) is the smallest number missing from the sequence.
%C A347769 This sequence is a permutation of the nonnegative integers iff Catalan's aliquot sequence conjecture (also called Catalan-Dickson conjecture) is true.
%C A347769 a(563) = 276 is the smallest number whose aliquot sequence has not yet been fully determined.
%C A347769 As long as the aliquot sequence of 276 is not known to be finite or eventually periodic, a(563+k) = A008892(k).
%H A347769 Eric Chen, <a href="/A347769/b347769.txt">Table of n, a(n) for n = 0..2703</a> (all currently known terms, after the b-file of A008892)
%H A347769 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AliquotSequence.html">Aliquot sequence</a>
%H A347769 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CatalansAliquotSequenceConjecture.html">Catalan's Aliquot Sequence Conjecture</a>
%H A347769 Wikipedia, <a href="https://en.wikipedia.org/wiki/Aliquot_sequence">Aliquot sequence</a>
%e A347769 a(0) = 0, a(1) = 1;
%e A347769 since A001065(a(1)) = 0 has already appeared in this sequence, a(2) = 2;
%e A347769 since A001065(a(2)) = 1 has already appeared in this sequence, a(3) = 3;
%e A347769 ...
%e A347769 a(11) = 11;
%e A347769 since A001065(a(11)) = 1 has already appeared in this sequence, a(12) = 12;
%e A347769 since A001065(a(12)) = 16 has not yet appeared in this sequence, a(13) = A001065(a(12)) = 16;
%e A347769 since A001065(a(13)) = 15 has not yet appeared in this sequence, a(14) = A001065(a(13)) = 15;
%e A347769 since A001065(a(14)) = 9 has already appeared in this sequence, a(15) = 13;
%e A347769 ...
%o A347769 (PARI) A347769_list(N)=print1(0, ", "); if(N>0, print1(1, ", ")); v=[0, 1]; b=1; for(n=2, N, if(setsearch(Set(v), sigma(b)-b), k=1; while(k<=n, if(!setsearch(Set(v), k), b=k; k=n+1, k++)), b=sigma(b)-b); print1(b, ", "); v=concat(v, b))
%Y A347769 Cf. A032451.
%Y A347769 Cf. A001065 (sum of aliquot parts).
%Y A347769 Cf. A003023, A044050, A098007, A098008: ("length" of aliquot sequences, four versions).
%Y A347769 Cf. A007906.
%Y A347769 Cf. A115060 (maximum term of aliquot sequences).
%Y A347769 Cf. A115350 (termination of the aliquot sequences).
%Y A347769 Cf. A098009, A098010 (records of "length" of aliquot sequences).
%Y A347769 Cf. A290141, A290142 (records of maximum term of aliquot sequences).
%Y A347769 Cf. A000396, A063990, A122726, A206708, A347770.
%Y A347769 Cf. A080907, A063769, A121507, A121508, A131884, A126016.
%Y A347769 Aliquot sequences starting at various numbers: A000004 (0), A000007 (1), A033322 (2), A010722 (6), A143090 (12), A143645 (24), A010867 (28), A008885 (30), A143721 (38), A008886 (42), A143722 (48), A143723 (52), A008887 (60), A143733 (62), A143737 (68), A143741 (72), A143754 (75), A143755 (80), A143756 (81), A143757 (82), A143758 (84), A143759 (86), A143767 (87), A143846 (88), A143847 (96), A143919 (100), A008888 (138), A008889 (150), A008890 (168), A008891 (180), A203777 (220), A008892 (276), A014360 (552), A014361 (564), A074907 (570), A014362 (660), A269542 (702), A045477 (840), A014363 (966), A014364 (1074), A014365 (1134), A074906 (1521), A143930 (3630), A072891 (12496), A072890 (14316), A171103 (46758), A072892 (1264460).
%K A347769 nonn
%O A347769 0,3
%A A347769 _Eric Chen_, Sep 13 2021