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 A221130 #8 Jun 13 2015 00:54:37 %S A221130 3,10,35,132,517,2054,8199,32776,131081,524298,2097163,8388620, %T A221130 33554445,134217742,536870927,2147483664,8589934609,34359738386, %U A221130 137438953491,549755813908,2199023255573,8796093022230,35184372088855,140737488355352,562949953421337 %N A221130 a(n) = 2^(2*n - 1) + n. %C A221130 Conjecture: a(n ) = the smallest numbers w such that numbers w, w+1,…, w+k-1 for k=1,2,…n are numbers of form h*2^m + m, where 1<=h <2^m, m = natural number (see A221129). %C A221130 a(5) = 517 because numbers 517, 518, 519, 520, 521 are numbers of presented form. %C A221130 517 = 16*2^5 + 5, 518 = 8*2^6 + 6, 519 = 4*2^7 + 7, 520 = 2*2^8 + 8, 521 = 1*2^9 + 9 (that is, numbers (2^(n-k))*(2^(n+k-1))+n+k-1, for k=1,2,,...n). %H A221130 Jaroslav Krizek, <a href="/A221130/b221130.txt">Table of n, a(n) for n = 1..53</a> %H A221130 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4) %F A221130 a(n+1) = a(n) + 3*2^(2*n-1)+1 = a(n) + 6*4^(n-1)+1 = a(n) + 2^(2*n+1) - 2^(2*n-1) + 1 = a(n) + A199116(n-1). %F A221130 G.f. -x*(3-8*x+2*x^2) / ( (4*x-1)*(x-1)^2 ). - _R. J. Mathar_, Jan 17 2013 %e A221130 a(5)=2^(2*5-1)+5=517. %Y A221130 Cf. A221129, A199116. %K A221130 nonn %O A221130 1,1 %A A221130 _Jaroslav Krizek_, Jan 02 2013