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

1,1

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.

Links

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

Example

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.

Mathematica

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

Crossrefs

Sequence in context: A084865 A047934 A090235 * A346052 A190197 A173631

Adjacent sequences: A265415 A265416 A265417 * A265419 A265420 A265421

Keyword

nonn

Author

Robert G. Wilson v, Dec 08 2015

Status

approved