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A126554 Arithmetic mean of two consecutive balanced primes (of order one). 7
29, 105, 165, 192, 234, 260, 318, 468, 578, 600, 630, 693, 840, 962, 1040, 1113, 1155, 1205, 1295, 1439, 1629, 1750, 1830, 2097, 2352, 2547, 2790, 2933, 3135, 3310, 3475, 3685, 3873, 4211, 4433, 4527, 4627, 4674, 4842, 5050, 5110, 5208, 5345, 5390, 5478 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Might be called interprimes of order two, since the arithmetic means of two consecutive odd primes (A024675) sometimes are called interprimes.

Balanced primes of order two (A082077) and doubly balanced primes (A051795) have different definitions.

For primes in this sequence (prime interprimes of order two) see A126555.

LINKS

Muniru A Asiru and Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Muniru A Asiru)

FORMULA

a(n) = (A006562(n+1)+A006562(n))/2.

MATHEMATICA

b = {}; a = {}; Do[If[PrimeQ[((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2], AppendTo[a, ((Prime[n + 2] + Prime[n + 1])/2 + (Prime[n + 1] + Prime[n])/2)/2]], {n, 1, 1000}]; Do[AppendTo[b, (a[[k + 1]] + a[[k]])/2], {k, 1, Length[a] - 1}]; b

PROG

(PARI) {m=6000; a=0; p=2; q=3; r=5; while(r<=m, if((p+r)/2==q, if(a>0, print1((a+q)/2, ", ")); a=q); p=q; q=r; r=nextprime(r+1))} \\ Klaus Brockhaus, Jan 05 2007

(GAP) P:=Filtered([1..6000], IsPrime);; P1:=List(Filtered(List([0..Length(P)-3], k->List([1..3], j->P[j+k])), i->Sum(i)/3=i[2]), m->m[2]);;

a:=List([1..Length(P1)-1], n->(P1[n+1]+P1[n])/2); # Muniru A Asiru, Mar 31 2018

CROSSREFS

Cf. A006562, A024675, A082077, A051795, A126555.

Sequence in context: A142138 A341550 A009435 * A258721 A009406 A211496

Adjacent sequences: A126551 A126552 A126553 * A126555 A126556 A126557

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 27 2006

EXTENSIONS

Edited by Klaus Brockhaus, Jan 05 2007

STATUS

approved

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Last modified January 31 05:03 EST 2023. Contains 359947 sequences. (Running on oeis4.)