A381287 a(n) is the smallest nonnegative number congruent to k modulo prime(k)^(n-k+1) for k=1..n.

1, 5, 353, 65153, 119966753, 3050486978753, 563678198162618753, 15413934869729743026218753, 1710386933322832904060816574218753, 14712401204424400291787297607394206774218753, 5027982881016562571248237683551040219315980699574218753, 5488604004979149030407333271782173318791620565366546226763574218753

Offset: 1

Author

Steven Lu, Feb 19 2025

Keywords

• nonn

Comments

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.

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.

Examples

			For n=3, a(3)=353 since 353 is the smallest nonnegative integer x satisfying:
  x == 1 (mod 2^3),
  x == 2 (mod 3^2),
  x == 3 (mod 5^1).
		

Links

• Steven Lu, Table of n, a(n) for n = 1..37

Crossrefs

Cf. A006939, A005687.

Programs

Mathematica

ToString[Table[ChineseRemainder[Range[n], (Prime /@ Range[n])^Range[n, 1, -1]], {n, 12}]]