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A152786 Integers n such that (n^2)/2 is the arithmetic mean of a pair of twin primes. 5
6, 12, 42, 48, 72, 84, 90, 174, 204, 264, 306, 372, 408, 456, 474, 546, 594, 600, 642, 750, 852, 882, 936, 972, 978, 1038, 1140, 1212, 1272, 1386, 1470, 1512, 1518, 1584, 1770, 1836, 1902, 1980, 1986, 2130, 2196, 2256, 2262, 2316, 2382, 2652, 2688, 2718 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Square roots of A054735 where these are integer.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..4288 (All terms up to 10^6.)

Zak Seidov, A152786 = 6*A037073: near-duplicates?, seqfan list, Aug 20 2010.

FORMULA

{n: n^2 = A054735(i), any i}. - R. J. Mathar, Dec 12 2008

a(n) = 6*A037073(n). [Zak Seidov, seqfan list, Aug 20 2010] [From R. J. Mathar, Sep 07 2010]

EXAMPLE

(6^2)/2=18= mean(17,19); (12^2)/2=72=mean(71,73); (42^2)/2=882=mean(881,883).

MATHEMATICA

lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; If[p2-p1==2, e=(2*(p1+1))^(1/2); i=Floor[e]; If[e==i, AppendTo[lst, i]]], {n, 3*9!}]; lst

(* Second program: *)

Select[Map[Sqrt[2 #] &, Mean /@ Select[Partition[Prime@ Range[10^6], 2, 1], Subtract @@ # == -2 &]], IntegerQ] (* Michael De Vlieger, Feb 18 2018 *)

PROG

(PARI) forstep(n=6, 1e3, 6, if(isprime(n^2/2-1)&&isprime(n^2/2+1), print1(n", "))) \\ Charles R Greathouse IV, Feb 01 2013

CROSSREFS

Cf. A014574, A037073, A152788 (cubic version).

Subsequence of A074924. - Zak Seidov, Feb 01 2013

Sequence in context: A307181 A052747 A007121 * A267309 A206039 A048069

Adjacent sequences:  A152783 A152784 A152785 * A152787 A152788 A152789

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 12 2008

EXTENSIONS

Edited by R. J. Mathar, Dec 12 2008

STATUS

approved

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Last modified December 7 18:12 EST 2019. Contains 329847 sequences. (Running on oeis4.)