login
A244066
Arithmetic mean of two consecutive twin primes that is also the arithmetic mean of two consecutive non-twin primes.
1
30, 42, 60, 105, 144, 165, 192, 228, 270, 312, 462, 570, 600, 858, 870, 882, 1026, 1092, 1230, 1254, 1290, 1302, 1428, 1482, 1620, 1878, 1998, 2028, 2340, 2550, 2688, 2730, 2760, 3345, 3540, 3582, 3627, 3795, 3885, 4020, 4338, 4500, 4518, 4650, 4755, 4788, 4866
OFFSET
1,1
COMMENTS
Intersection of A162734 (averages of consecutive non-twin primes) and A163656 (averages of consecutive twin primes).
a(n)/3 are: 10, 14, 20, 35, 48, ...
LINKS
EXAMPLE
30 is in this sequence because it is the arithmetic mean of 29 and 31, consecutive terms of A001097, as well as of 23 and 37, consecutive terms of A007510.
MATHEMATICA
Module[{prs=Prime[Range[800]], tp, nt}, tp=Flatten[Select[Partition[ prs, 2, 1], #[[2]]- #[[1]]==2&]]; nt=Complement[prs, tp]; Select[Tally[ Join[ Mean/@ Partition[tp, 2, 1], Mean/@Partition[nt, 2, 1]]], #[[2]]==2&][[All, 1]]] (* Harvey P. Dale, Sep 03 2016 *)
PROG
(PARI)
a244066(pmax) = {
my(tp=[], m, j, k, s=[]);
forprime(p=2, pmax, if(isprime(p-2) || isprime(p+2), tp=concat(tp, p)));
for(i=1, #tp-1,
m=(tp[i]+tp[i+1])\2;
j=1; while(!(isprime(m+j) && !isprime(m+j-2) && !isprime(m+j+2)), j++);
k=1; while(!(isprime(m-k) && !isprime(m-k-2) && !isprime(m-k+2)), k++);
if(j==k, s=concat(s, m))
);
s
}
a244066(5000) \\ Colin Barker, Jul 18 2014
CROSSREFS
Cf. A014574, A007510. Subsequence of A163656.
Sequence in context: A302753 A179945 A136152 * A090815 A238367 A225228
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by Antti Karttunen, Jun 21 2014.
Terms and definition corrected by Colin Barker, Jul 18 2014
STATUS
approved