This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217259 #29 May 21 2018 03:14:48 %S A217259 4,6,12,18,30,42,60,72,102,108,138,150,180,192,198,228,240,270,282, %T A217259 312,348,420,432,435,462,522,570,600,618,642,660,810,822,828,858,882, %U A217259 1020,1032,1050,1062,1092,1152,1230,1278,1290,1302,1320,1428,1452,1482,1488 %N A217259 Numbers n such that sigma(n+1) - sigma(n-1) = 2; sigma(n) = A000203(n) = sum of divisors of n. %C A217259 Also numbers n such that antisigma(n+1) - antisigma(n-1) = 2*n - 1. %C A217259 Antisigma(n) = A024816(n) = sum of nondivisors of n. %C A217259 Union of A014574 (average of twin prime pairs) and sequence 435, 8576, 8826, … (= all terms < 100000). %C A217259 If n = average of twin prime pairs (q < p) then antisigma(p) - antisigma(q) = 2*n - 1 = p + q - 1. %C A217259 No term found below 2*10^9 to continue sequence 435, 8576, 8826, ... - _Michel Marcus_, Mar 19 2013 %H A217259 Jaroslav Krizek, <a href="/A217259/b217259.txt">Table of n, a(n) for n = 1..1227</a> (all terms < 100000) %e A217259 Number 435 is in sequence because antisigma(436) - antisigma(434) = 94496 - 93627 = 869 = 2*435 - 1. %t A217259 Flatten[Position[Partition[DivisorSigma[1,Range[1500]],3,1],_?(#[[3]]- #[[1]] == 2&),1,Heads->False]]+1 (* _Harvey P. Dale_, May 03 2018 *) %o A217259 (PARI) isok(n) = (sigma(n+1) - sigma(n-1)) == 2; \\ _Michel Marcus_, May 20 2018 %Y A217259 Cf. A014574, A015886, A024816, A050507, A206768. %Y A217259 Equals A054799 + 1. - _Michel Marcus_, May 21 2018 %K A217259 nonn %O A217259 1,1 %A A217259 _Jaroslav Krizek_, Mar 17 2013