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 A155072 #29 Jun 27 2025 16:21:43
%S A155072 17,41,97,137,193,313,401,409,449,521,569,761,769,809,857,929,977,
%T A155072 1009,1129,1297,1361,1409,1489,1697,1873,1993,2081,2137,2153,2161,
%U A155072 2297,2377,2417,2521,2609,2617,2633,2713,2729,2753,2777,2801,2897,3001
%N A155072 Positive integers n such that the base-2 MR-expansion of 1/n is periodic with period (n-1)/4.
%C A155072 See A136042 for the definition of the MR-expansion of a positive real number.
%C A155072 It appears that all terms of this sequence are primes of the form 8n+1 (A007519).
%C A155072 Apparently a subsequence of A115591. - _Mia Boudreau_, Jun 17 2025
%H A155072 Mia Boudreau, <a href="/A155072/b155072.txt">Table of n, a(n) for n = 1..1000</a>
%e A155072 Applying the definition of the base-2 MR-expansion to 1/17 gives 1/17 -> 2/17 -> 4/17 -> 8/17 -> 16/17 -> 32/17 -> 15/17 -> 30/17 -> 13/17 -> 26/17 -> 9/17 -> 18/17 -> 1/17 -> ..., which shows that the expansion begins {5,1,1,1,...} and has period 4=(17-1)/4.
%t A155072 a[p_] := 1 + Sum[2 Cos[2^n Pi/((2 p + 1) )], {n, 1, p}];
%t A155072 Select[Range[500], Reduce[a[#]^2 == 2 # + 1, Integers] &];
%t A155072 2 % + 1 (* _Gerry Martens_, May 01 2016 *)
%Y A155072 Cf. A136042, A007519, A115591, A136043.
%K A155072 nonn
%O A155072 1,1
%A A155072 _John W. Layman_, Jan 19 2009
%E A155072 More terms from _Mia Boudreau_, Jun 17 2025