OFFSET
1,1
COMMENTS
Conjectures and open problems: 1) It is not known whether the sequence is infinite; 2) It is conjectured that for every n there is corresponding a(n). If Conjecture 2) were proved, Conjecture 1) would follow as a direct consequence.
a(50) > 10^10. - Donovan Johnson, Jan 25 2012
Note that the sequence appears to undulate with terms that satisfy a(2n-1) < a(2n) < a(2n+1). Is there an explanation? - Michel Marcus, Nov 21 2013
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..49
Art of Problem Solving, Gaps in {sigma(n)}...
EXAMPLE
a(2)=16 because 16,17 are not contained in values of sigma(k) and 15,18 are; namely: sigma(8)=15 and sigma(10)=18, where sigma(k)=sum of all positive divisors of k.
PROG
(PARI) oksuccs(v, vi, n) = {for (i = 1, n-1, if (! vecsearch(v, vi+i, ) , return (0)); ); return(! vecsearch(v, vi-1) && !vecsearch(v, vi+n)); }
a(n) = {v = readvec("suntouch2.log"); for (i=1, #v, vi = v[i]; if (oksuccs(v, vi, n), return(vi)); ); } \\ where file read by readvec is the second column of b-file. Michel Marcus, Nov 21 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Bojan Basic (bbasic(AT)ptt.yu), Sep 18 2005
STATUS
approved