cp's OEIS Frontend

A110875 Minimum positive integer such that length of the gap described at A109322 is exactly n (in contrast to A109322 where the gap length is >= n).

%I A110875 #25 Apr 30 2025 23:12:35
%S A110875 2,16,9,64,49,872,481,1768,423,2980,1333,49180,5335,46666,4425,86815,
%T A110875 8763,1109259,14089,658513,29883,137539,22825,10927365,259843,1667974,
%U A110875 46773,7698572,40291,16048081,178705,16039804,1135023,132082042,661285,525395164
%N A110875 Minimum positive integer such that length of the gap described at A109322 is exactly n (in contrast to A109322 where the gap length is >= n).
%C A110875 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.
%C A110875 a(50) > 10^10. - _Donovan Johnson_, Jan 25 2012
%C A110875 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
%H A110875 Donovan Johnson, <a href="/A110875/b110875.txt">Table of n, a(n) for n = 1..49</a>
%H A110875 Art of Problem Solving, <a href="https://artofproblemsolving.com/community/c6h26906">Gaps in {sigma(n)}...</a>
%e A110875 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.
%o A110875 (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));}
%o A110875 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
%Y A110875 Cf. A109322, A109323, A109324.
%Y A110875 Cf. A231965 (analog for sigma(n) - n).
%K A110875 nonn
%O A110875 1,1
%A A110875 Bojan Basic (bbasic(AT)ptt.yu), Sep 18 2005