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A218014 Location of the n-th prime in its Andrica ranking. 2
27, 6, 13, 1, 31, 4, 54, 8, 3, 100, 5, 25, 155, 28, 9, 16, 243, 19, 49, 288, 21, 62, 24, 12, 75, 422, 81, 444, 84, 2, 112, 37, 580, 11, 634, 47, 53, 150, 57, 60, 788, 20, 840, 183, 872, 10, 14, 218, 1029, 228, 80, 1074, 26, 87, 92, 99, 1237, 103, 281, 1319, 29, 15, 314, 1498, 323 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For each consecutive prime pair p < q, d = sqrt(q) - sqrt(p) is unique. Place d in order from greatest to least and specify p.

Last appearance by prime index: 1, 5, 7, 10, 13, 17, 20, 26, 28, 33, 35, 41, 43, 45, 49, ..., .

Last appearance of a minimum prime by Andrica ranking: 2, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, ..., .

As expected, this sequence is the lesser of the twin primes beginning with the second term, 11. See A001359.

LINKS

Table of n, a(n) for n=1..65.

Marek Wolf, A Note on the Andrica Conjecture, arXiv:1010.3945 [math.NT], 2010.

EXAMPLE

a(1)=27 since the first prime, 2, does not show up in the ranking until the 27th term. See A218013.

a(4)=1 since the fourth prime, 7, has the maximum A_n value, see A218012; i.e., sqrt(p_n)-sqrt(p_n+1) is at a maximum.

MATHEMATICA

lst = {}; p = 2; q = 3; While[p < 1600000, If[ Sqrt[q] - Sqrt[p] > 1/20, AppendTo[lst, {p, Sqrt[q] - Sqrt[p]}]]; p = q; q = NextPrime[q]]; lsu = First@ Transpose@ Sort[lst, #1[[2]] > #2[[2]] &]; Table[ Position[lsu, p, 1, 1], {p, Prime@ Range@ 65}] // Flatten

CROSSREFS

Cf. A079296, A218012, A218015.

Sequence in context: A175240 A204877 A040709 * A040710 A040708 A214103

Adjacent sequences:  A218011 A218012 A218013 * A218015 A218016 A218017

KEYWORD

nonn

AUTHOR

Marek Wolf and Robert G. Wilson v, Oct 18 2012

STATUS

approved

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Last modified November 30 14:59 EST 2020. Contains 338802 sequences. (Running on oeis4.)