Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #11 Nov 04 2013 04:17:27
%S 55,6,7,12,173,6,173,6,205,6,229,6,113,6,203,6,95,6,475,6,163,6,119,
%T 12,377,18,1045,6,133,12,551,24,131,12,259,6,1105,42,539,6,1487,18,
%U 1295,12,5,12,289,36,311,36,269,6,2833,6,1813,18,835,6,319,6,587,6,239,30,1225,6,1825,12,973,12,89,30,551,12,1805,30,1039,18,1219,6
%N Sequence of pairs k,g with k<3*2^n the smallest such that 3*2^n+k, 3*2^n+k+g, 3*2^n+k+2*g are three consecutive primes in arithmetic progression starting at n=5 as there is not any solution for n<5
%C The ratio k/n^2 is in average near 0.8 and < 7 for n<701.
%C The ratio g/n^2 is in average near 0.5 and < 4 for n<701.
%C If 3*2^n+k > 10^22 the numbers are probable primes.
%H Pierre CAMI, <a href="/A227856/b227856.txt">Table of n, a(n) for n = 5..1396</a>
%e 3*2^5+55=151, 3*2^5+55+6=157 3*2^5+55*2*6=163
%e 151, 157, 163 three consecutive primes in arithmetic progression 6, so first pair is 55, 6
%o PFGW & SCRIPTIFY
%o SCRIPT
%o DIM i
%o DIM j
%o DIM k
%o DIM n,4
%o DIM pp
%o DIM qq
%o DIM rr
%o DIMS t
%o OPENFILEOUT myf,a(n).txt
%o LABEL loop1
%o SET n,n+1
%o SET i,-1
%o SET j,0
%o SET k,0
%o LABEL a
%o SET i,i+2
%o SETS t,%d,%d\,;n;i
%o SET pp,3*2^n+i
%o PRP pp,t
%o IF ISPRP THEN GOTO b
%o GOTO a
%o LABEL b
%o SET j,j+2
%o SETS t,%d,%d,%d\,;n;i;j
%o SET qq,pp+j
%o PRP qq,t
%o IF ISPRP THEN GOTO c
%o GOTO b
%o LABEL c
%o SET k,k+2
%o SETS t,%d,%d,%d,%d\,;n;i;j;k
%o SET rr,qq+k
%o PRP rr,t
%o IF ISPRP THEN GOTO d
%o GOTO c
%o LABEL d
%o IF j==k THEN GOTO x
%o SET i,i+j
%o SET pp,qq
%o SET j,0
%o SET k,0
%o GOTO b
%o LABEL x
%o WRITE myf,t
%o GOTO loop1
%Y Cf. A230699, A230852
%K nonn
%O 5,1
%A _Pierre CAMI_, Nov 01 2013