The On-Line Encyclopedia of Integer Sequences (OEIS)

A370161 revision #3

A370161

Numerator of fraction a(n)/b(n) < 3, where a(n) and b(n) are primes, and if p is a prime <= b(n) such that k/p < 3 for some prime k, then k = a(n) and p = b(n).

5, 13, 19, 31, 37, 67, 109, 127, 139, 157, 181, 199, 211, 307, 337, 379, 409, 487, 499, 541, 571, 577, 631, 751, 769, 787, 811, 829, 877, 919, 937, 991, 1009, 1039, 1117, 1201, 1291, 1297, 1327, 1381, 1399, 1459, 1471, 1567, 1621, 1669, 1759, 1777, 1801

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OFFSET

1,1

COMMENTS

(a(n)/(b(n)) is a strictly increasing sequence that converges to 3.

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

5/2 < 13/5 < 19/7 < 31/11 < 37/13 < 67/23 < 109/37 < 127/43 < 139/47 < ...

MATHEMATICA

a = {{4, 4}}; r = 3; Do[If[# < Last[a][[2]], AppendTo[a, {n, #}]] &[

NextPrime[Prime[PrimePi[Prime[n]*r]]]/Prime[n]], {n, 1300}];