A109324 -id:A109324 - 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).

2, 16, 9, 64, 49, 872, 481, 1768, 423, 2980, 1333, 49180, 5335, 46666, 4425, 86815, 8763, 1109259, 14089, 658513, 29883, 137539, 22825, 10927365, 259843, 1667974, 46773, 7698572, 40291, 16048081, 178705, 16039804, 1135023, 132082042, 661285, 525395164

Offset: 1

Bojan Basic (bbasic(AT)ptt.yu), Sep 18 2005

nonn

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

			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.

Donovan Johnson, Table of n, a(n) for n = 1..49
Art of Problem Solving, Gaps in {sigma(n)}...

Cf. A109322, A109323, A109324.

Cf. A231965 (analog for sigma(n) - n).

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

A109322 a(n) is the minimum positive integer j such that [j, j+n-1] does not contain any values of sigma(k) (i.e., sum of all positive divisors of k).

Original entry on oeis.org

2, 9, 9, 49, 49, 423, 423, 423, 423, 1333, 1333, 4425, 4425, 4425, 4425, 8763, 8763, 14089, 14089, 22825, 22825, 22825, 22825, 40291, 40291, 40291, 40291, 40291, 40291, 178705, 178705, 661285, 661285, 661285, 661285, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141, 4543141

Offset: 1

Max Alekseyev and Jud McCranie, Aug 08 2005

nonn

Donovan Johnson, Table of n, a(n) for n = 1..85 (terms < 10^10)
Art of Problem Solving, Gaps in {sigma(n)}...

Cf. A002191, A083531, A109323, A109324, A110875.

A109323 A109322 with duplicates removed.

Original entry on oeis.org

2, 9, 49, 423, 1333, 4425, 8763, 14089, 22825, 40291, 178705, 661285, 4543141, 20706715, 29243521, 31089603, 32341621, 99158905, 417976441, 1186496401, 1540962199, 2097064537, 8602909969

Offset: 1

Max Alekseyev and Jud McCranie, Aug 08 2005

Cf. A109322, A109324, A110875.

a(20)-a(23) from Donovan Johnson, Jan 25 2012

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).

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A109322 a(n) is the minimum positive integer j such that [j, j+n-1] does not contain any values of sigma(k) (i.e., sum of all positive divisors of k).

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A109323 A109322 with duplicates removed.

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