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 A308782 #23 Dec 24 2021 08:12:22 %S A308782 2,0,8,50,132,414,171,659,96,361,12311,7224,5896,2954,5804,72387, %T A308782 12756,1292,4332,3715,2704,1887,5780,9837,11721,1094,70067,32610, %U A308782 57658,26146,167389,94957,36588,19663,35588,9627,108296,51653,38147,54788,81871,15502 %N A308782 Index of first occurrence of n appearing twice in succession in van Eck's sequence (A181391), or 0 if it never occurs. %C A308782 With V=A181391, a(n) is the smallest number m such that V(m) = V(m-1) = n. %C A308782 Since van Eck's sequence is generated by considering the gap between identical terms reappearing, it is of interest to consider terms of value n which repeat with a gap of length n. %C A308782 When this happens the term is repeated in succession. %C A308782 Some observations that follow from the definition of V: %C A308782 V(a(n)-1-n) = n. The value n has to appear exactly n terms apart in V to make the following term equal to n, e.g., for n=3: "..., 3, 8, 0, 3, 3, ...". %C A308782 V(a(n)+1) = 1. Since the term n appeared twice in a row, the following term of V must be 1. %C A308782 V(a(n)-2) = V(a(n)-n-2) = V(a(n)-2*n-2). The number preceding the repeated terms appears three times with gaps of n. %C A308782 V(a(n)+2) = the number of terms since the previous repeated value of some number (though it may not be the first time it is repeated). So V(a(n)-V(a(n)+2)) = V(a(n)-V(a(n)+2)-1). %H A308782 Rémy Sigrist, <a href="/A308782/b308782.txt">Table of n, a(n) for n = 0..999</a> %H A308782 Rémy Sigrist, <a href="/A308782/a308782.txt">C++ program for A308782</a> %e A308782 With V=A181391 and n=8: %e A308782 V(95) = V(96) = 8. Therefore, a(8) = 96. %e A308782 --- %e A308782 V(a(n)-1-n) = n: %e A308782 a(8) - 1 - 8 = 87. %e A308782 V(87) = 8. %e A308782 --- %e A308782 V(a(n)+1) = 1: %e A308782 a(8) + 1 = 97. %e A308782 V(97) = 1. %e A308782 --- %e A308782 V(a(n)-2) = V(a(n)-n-2) = V(a(n)-2*n-2): %e A308782 a(8) - 2 = 94. %e A308782 a(8) - 8 - 2 = 86. %e A308782 a(8) - 2*8 - 2 = 78. %e A308782 V(94) = V(86) = V(78) = 3. %e A308782 --- %e A308782 V(a(8)+2) = 46. a(8) - 46 = 50. The previous repeated terms in V are V(50) = V(49) = 5. %o A308782 (C++) See Links section. %Y A308782 Cf. A181391 (van Eck's sequence). %K A308782 nonn %O A308782 0,1 %A A308782 _Deron Stewart_, Jun 24 2019