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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 10:07 EDT 2021. Contains 346289 sequences. (Running on oeis4.)