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 A345473 #23 Oct 02 2021 19:15:15 %S A345473 6,56,236,956,2636,3356,6236,9716,10196,13436,15896,18296,24716,26396, %T A345473 36116,36956,37196,42956,53036,69356,82556,84536,119516,121496,181556, %U A345473 201116,204236,221756,252116,259676,332636,359036,365036,401516 %N A345473 Given the associative array U(n,k) described below, numbers m > 5 such that [m-3..m+3] are not in U(n,k) (excluding the first row and column). %C A345473 U(n,k) is a commutative and associative array with integer values that depend on whether n and k are odd or even. %C A345473 U(n,k) = (5*n*k - 3*(n+k-1))/2 when n and k are both odd. %C A345473 U(n,k) = (5*n*k - 3*n)/2 when n is even and k is odd. %C A345473 U(n,k) = (5*n*k - 3*k)/2 when n is odd and k is even. %C A345473 U(n,k) = 5*n*k/2 when n and k are both even. %C A345473 U(n,1) = n for all n (identity element). %C A345473 U(n,0) = 0 for all n. %C A345473 The ordered list of numbers >5 that do not appear in array U(n,k) for n and k > 1 can have at most 3 consecutive even numbers and at most 5 consecutive odd numbers. See rows 2 and 3. %C A345473 The terms all end in 6 because row 2 of U(n,k) has all numbers that end in 0 or 2 and there are at most 3 consecutive even numbers in the set of numbers not in array U(n,k) excluding the first row and column (see comment for A327263). %C A345473 There are 119 terms up to 5*10^6. %H A345473 David Lovler, <a href="/A345473/b345473.txt">Table of n, a(n) for n = 1..119</a> %e A345473 Array U(n,k) begins: %e A345473 1 2 3 4 5 6 7 8 9 10 %e A345473 2 10 12 20 22 30 32 40 42 50 %e A345473 3 12 15 24 27 36 39 48 51 60 %e A345473 4 20 24 40 44 60 64 80 84 100 %e A345473 5 22 27 44 49 66 71 88 93 110 %e A345473 6 30 36 60 66 90 96 120 126 150 %e A345473 7 32 39 64 71 96 103 128 135 160 %e A345473 8 40 48 80 88 120 128 160 168 200 %e A345473 9 42 51 84 93 126 135 168 177 210 %e A345473 10 50 60 100 110 150 160 200 210 250 %e A345473 Numbers up to 100 not in U(n,k) (excluding row 1 and column 1): 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 16, 17, 18, 19, 21, 23, 25, 26, 28, 29, 31, 33, 34, 35, 37, 38, 41, 43, 45, 46, 47, 53, 54, 55, 56, 57, 58, 59, 61, 65, 67, 68, 69, 73, 74, 76, 77, 78, 79, 81, 83, 85, 86, 89, 91, 94, 95, 97, 98. %o A345473 (PARI) T319929(n, k) = if (n%2, if (k%2, n+k-1, k), if (k%2, n, 0)); %o A345473 U(n, k) = (5*n*k - 3*T319929(n, k))/2; %o A345473 list(nn) = {my(list = List()); for (n=2, nn, for (k=2, nn\n, listput(list, U(n, k)); ); ); setminus([1..nn], Set(list)); } %o A345473 lista(nn) = {my(v=Vec(list(nn))); for (m=6, #v-1, my(x=v[m]); if (#setintersect(v,[x-3..x+3])==7, print1(x, ", ")); ); } %Y A345473 In A327263 U(n,k) is called U(5;n,k). %Y A345473 Cf. A340748, A345357, A345474. %K A345473 nonn %O A345473 1,1 %A A345473 _David Lovler_, Jun 21 2021