# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a306285 Showing 1-1 of 1 %I A306285 #33 Sep 09 2022 22:26:09 %S A306285 4,21,30,47,56,73,82,99,108,125,134,151,160,177,186,203,212,229,238, %T A306285 255,264,281,290,307,316,333,342,359,368,385,394,411,420,437,446,463, %U A306285 472,489,498,515,524,541,550,567,576,593,602,619,628,645,654,671,680,697,706,723,732,749,758,775,784,801,810,827,836,853,862 %N A306285 Numbers congruent to 4 or 21 mod 26. %C A306285 A007310(a(n)+1) is always a multiple of 13. %C A306285 a(n) mod 6 follows the following pattern: 4,3,0,5,2,1,4,3,0,5,2,1 and so on. %C A306285 a(n) mod 4 = A010873(n) %C A306285 A020639(A007310(a(n)+1) = 5 when n is congruent to 2 or 9 (mod 10) (n is a term in A273669). It equals 7 when n is congruent to 3 or 12 (mod 14) but not congruent to 2 or 9 (mod 10). It equals 11 when n is congruent to 4 or 19 (mod 22) but not congruent to 2 or 9 (mod 10) and not congruent to 3 or 12 (mod 14). Otherwise, it is 13. %H A306285 Davis Smith, Table of n, a(n) for n = 1..1000 %H A306285 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). %F A306285 a(n) = 13*n - A010720(n+1). %F A306285 From _Colin Barker_, Feb 08 2019: (Start) %F A306285 G.f.: x*(4 + 17*x + 5*x^2) / ((1 - x)^2*(1 + x)). %F A306285 a(n) = 13*n - 5 for n even. %F A306285 a(n) = 13*n - 9 for n odd. %F A306285 a(n) = a(n-1) + a(n-2) - a(n-3) for n>3. (End) %F A306285 E.g.f.: 5 + (13*x - 7)*exp(x) + 2*exp(-x). - _David Lovler_, Sep 09 2022 %p A306285 seq(seq(26*i+j, j=[4, 21]), i=0..200); %t A306285 Select[Range[200], MemberQ[{4, 21}, Mod[#, 26]] &] %o A306285 (PARI) for(n=1, 1000, if((n%26==4) || (n%26==21), print1(n, ", "))) %o A306285 (PARI) Vec(x*(4 + 17*x + 5*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ _Colin Barker_, Feb 08 2019 %Y A306285 Cf. A007310, A010720, A020639, A010873, A273669. %K A306285 nonn,easy %O A306285 1,1 %A A306285 _Davis Smith_, Feb 03 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE