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A234842 Primes that are reached by an ever increasing aliquot sequence.

%I A234842 #32 Nov 04 2024 04:24:24
%S A234842 463,523,983,1153,2851,2969,4339,4507,6121,8263,8893,10093,12451,
%T A234842 17911,18427,18913,22807,22811,25033,27961,33223,36781,41849,42643,
%U A234842 48571,60091,64237,71503,73303,74131,90217,90481,103813,108263,123601,124447,125863,140443
%N A234842 Primes that are reached by an ever increasing aliquot sequence.
%C A234842 Note that the starting point of these aliquot sequences are not in increasing order, since for instance we have: 392->463->1 and 324->523->1, that is, with 392>324 while 463<523.
%C A234842 One can observe that the "ever increasing aliquot" part in the definition is not really necessary. A prime is in the sequence if there is an abundant number whose sum of proper divisors results into this prime. So sequence could also be defined as: Primes resulting from summing up the proper divisors of an abundant number. - _Michel Marcus_, Jan 05 2014
%C A234842 If we try to build the revert sequence listing the starting points of the aliquot sequences, we would get the following terms in increasing order 324, 392, 784, 800, 2304, 2450, 2704, 3600, 3872. But then for n=5352, we'd hit a sequence that begins 5352->8088->12192->20064 and keeps rising to a point where the factors of the last known term are not known. Then later, there are several other such aliquot sequences like 9336->14064->22392 or 10344->15576->27624 that have the same behavior. Thus the only sure terms of the revert sequence would be the terms listed earlier. - _Michel Marcus_, Jan 11 2014
%H A234842 Michel Marcus, <a href="/A234842/b234842.txt">Table of n, a(n) for n = 1..100</a>
%H A234842 Factordb, <a href="http://factordb.com/sequences.php?se=1&amp;aq=14952&amp;action=all">Sequence starting with 14952</a>
%H A234842 Michel Marcus, <a href="/A234842/a234842.txt">Aliquot sequences leading to these primes</a>
%H A234842 <a href="http://www.mersenneforum.org/showthread.php?t=19049">Help needed for a sequence </a> Thread on Aliquot Sequences Forum
%e A234842 The aliquot sequence that begins with 10712 is always increasing before reaching prime 12451: 10712->11128->11552->12451->1, hence 12451 is in the sequence.
%e A234842 20422951 also belongs here with the aliquot sequence that starts at 14952, so a 13-tuple abundant (see factordb link).
%e A234842 People at the Aliquot Sequences project have found longer sequences that reach higher primes.
%o A234842 (PARI) prev(n) = {for (i=1, n, if ((sigma(i) - i) == n, return (i));); return (0);}
%o A234842 lista(nn) = {forprime(p=2, nn, if (prev(p), print1(p, ", ");););} \\ simplified by _Michel Marcus_, Jan 11 2014
%Y A234842 Cf. A001065, A005101, A080907, A081705, A098007, A098008, A115350.
%K A234842 nonn
%O A234842 1,1
%A A234842 _Michel Marcus_, Dec 31 2013