A265418 a(1)=2; for n>1, a(n) is the least prime q greater than p = a(n-1) such that p/q reaches a new minimum.

2, 3, 5, 11, 29, 79, 223, 631, 1787, 5077, 14431, 41023, 116639, 331651, 943031, 2681467, 7624649, 21680413, 61647497, 175292519, 498438203, 1417291781, 4030020143, 11459222851, 32583903763, 92651203181, 263450491193, 749112358279, 2130075077051, 6056794796849, 17222286484817

Offset: 1

Author

Robert G. Wilson v, Dec 08 2015

Keywords

• nonn

Comments

Inspired by the fact that 294911/235927 = 1.2500095368..., two primes together with 2^16 form a primitive weird number (A002975(9729)).

p/q ->

0.3516835469078526298668938767771073728

...

Each pair of initial primes, p & q, will yield a different ratio.

Examples

			2/3 is 0.666... is a new low or minimum;
3/5 is 0.600... is a new minimum;
5/11 is 0.454... is a new minimum;
11/29 is 0.379... is a new minimum;
29/79 is 0.367... is a new minimum;
... 6056794796849/17222286484817 is 0.351... is a new minimum; etc.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1620

Programs

Mathematica

f[lst_List] := Block[{p = lst[[-2]], q = lst[[-1]]}, Append[lst, NextPrime[q^2/p]]]; Nest[f, {2, 3}, 29]