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 A381287 #34 Mar 15 2025 04:23:18
%S A381287 1,5,353,65153,119966753,3050486978753,563678198162618753,
%T A381287 15413934869729743026218753,1710386933322832904060816574218753,
%U A381287 14712401204424400291787297607394206774218753,5027982881016562571248237683551040219315980699574218753,5488604004979149030407333271782173318791620565366546226763574218753
%N A381287 a(n) is the smallest nonnegative number congruent to k modulo prime(k)^(n-k+1) for k=1..n.
%C A381287 This sequence is an example demonstrating how an integer sequence (thus a rational number sequence) converges to distinct limits in all p-adic systems; that is, converges to 1 in 2-adic, to 2 in 3-adic, to k in prime(k)-adic, and so on.
%C A381287 Moreover, the rational number sequence a(n) / prime(n+1) ^ (primorial(n)^(n-1) * A005867(n)) converges to distinct limits in all p-adic systems as well as the real number system, with limit zero in real numbers, and limit k in prime(k)-adic, where k is any positive integer.
%H A381287 Steven Lu, <a href="/A381287/b381287.txt">Table of n, a(n) for n = 1..37</a>
%e A381287 For n=3, a(3)=353 since 353 is the smallest nonnegative integer x satisfying:
%e A381287 x == 1 (mod 2^3),
%e A381287 x == 2 (mod 3^2),
%e A381287 x == 3 (mod 5^1).
%t A381287 ToString[Table[ChineseRemainder[Range[n], (Prime /@ Range[n])^Range[n, 1, -1]], {n, 12}]]
%Y A381287 Cf. A006939, A005687.
%K A381287 nonn
%O A381287 1,2
%A A381287 _Steven Lu_, Feb 19 2025