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 A327714 #22 Aug 11 2025 07:03:37 %S A327714 73,98,99,112,141,154,171,197,225,245,266,276,283,288,290,301,309,316, %T A327714 322,323,330,357,385,386,406,414,444,455,463,465,483,484,491,498,512, %U A327714 525,539,554,575,596,602,626,654,665,679 %N A327714 Exceptional class of numbers k such that p(7*k + 5) == 0 (mod 49), where p() = A000041(). %C A327714 The unexceptional class consists of the numbers k == (2, 4, 5, or 6) (mod 7). Watson (1938, p. 125) proved that such numbers k satisfy p(7*k + 5) == 0 (mod 49). %H A327714 Watson, G. N., <a href="https://gdz.sub.uni-goettingen.de/id/PPN243919689_0179">Ramanujans Vermutung über Zerfällungsanzahlen</a>, J. Reine Angew. Math. (Crelle) 179 (1938), 97-128; see pp. 124-127. %e A327714 p(7*73 + 5) = p(516) = 49 * 113094142490063549717. This example is given by Watson (1938, p. 127). On the same page, he also says that p(105*7 + 5) = p(740) == 0 (mod 49) (even though 105 == 0 (mod 7)), but that is wrong. %p A327714 isA327714 := n -> 0 = modp(combinat:-numbpart(7*n + 5), 49) and 2 <> modp(n, 7) and 4 <> modp(n, 7) and 5 <> n mod 7 and 6 <> n mod 7; %p A327714 select(isA327714, [$ (1 .. 700)]); %Y A327714 Cf. A000041, A110375, A160524, A327713. %K A327714 nonn %O A327714 1,1 %A A327714 _Petros Hadjicostas_, Sep 23 2019