A387354 a(n) = least prime m such that m/prime(n) > a(n-1)/prime(n-1), where a(1) = 3.

3, 5, 11, 17, 29, 37, 53, 61, 79, 101, 109, 131, 149, 157, 173, 197, 223, 233, 257, 277, 293, 331, 349, 379, 419, 439, 449, 467, 479, 499, 563, 587, 617, 631, 677, 691, 719, 751, 773, 809, 839, 853, 907, 919, 941, 953, 1013, 1087, 1109, 1123, 1151, 1181

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

These are the numerators in this chain of prime-fractions: 3/2 < 5/3 < 11/5 < 17/7 < ... .

Mathematica

p[n_] := Prime[n]; m[1] = 3;
m[n_] := m[n] = NextPrime[Floor[m[n - 1] p[n]/p[n - 1]]]
Table[m[n], {n, 1, 100}]

Prog

(PARI) lista(nn) = my(va=vector(nn)); va[1] = 3; for (n=2, nn, va[n] = nextprime(va[n-1]*prime(n)/prime(n-1)); ); va; \\ Michel Marcus, Sep 11 2025

Crossrefs

Cf. A000040.

Sequence in context: A066692 A123533 A144105 * A141262 A069233 A329946

Adjacent sequences: A387351 A387352 A387353 * A387355 A387356 A387357

Keyword

nonn

Author

Clark Kimberling, Aug 27 2025

Status

approved