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%I #9 Aug 07 2015 02:57:41
%S 3,5,11,17,5,11,17,29,41,59,71,101,107,137,149,179,191,197,29,59,149,
%T 179,239,269,419,569,599,659,809,1019,1049,1229,1319,1619,1949,2129,
%U 419,1049,2309,2729,3359,5879,6089,6299,7349,7559,8819,9239,10499,10709
%N Table read by rows where row n contains lower twin primes of the form k*A002110(n)-1 in the range 0 < k < A006094(n+1).
%C Some of the values k*primorial(n)-1 generated by k in the range 1 to prime(n+1)*prime(n+2)-1 are not lower twin primes, A001359, so the list of k that produces the n-th row of the irregular table, as shown in A088329, is not a list of necessarily consecutive integers.
%C If n>2 the count of k values is near or greater than 4*log(4*p(n+1)); is this related to a proof of the infinity of twin prime pairs?
%e 2*2 -1 = 3, k=2, n=1
%e 3*2 -1 = 5, k=3, n=1
%e 6*2 -1 = 11, k=6, n=1
%e 9*2 -1 = 17, k=9, n=1
%e The first three rows are:
%e 3,5,11,17; generated by k=2, 3, 6, 9
%e 5,11,17,29,41,59,71,101,107,137,149,179,191,197;
%e 29,59,149,179,239,269,419,569,599,659,809,1019,1049,1229,1289,1319,1619,1949,2129;
%p isA001359 := proc(n) option remember ; return isprime(n) and isprime(n+2) ; end:
%p A002110 := proc(n) local i ; if n = 0 then 1; else mul(ithprime(i),i=1..n) ; end if; end proc:
%p A006094 := proc(n) return ithprime(n)*ithprime(n+1) ; end proc:
%p A088328 := proc(n,k) option remember; for j from 1 to A006094(n+1)-1 do a := j*A002110(n)-1 ; if isA001359(a) and k =1 then return a ; elif isA001359(a) and a > procname(n,k-1) then return a ; end if; end do; return -1 ; end proc:
%p for n from 1 to 10 do for k from 1 do T := A088328(n,k) ; if T < 0 then break; else printf("%d,",T) ; end if; end do; printf("\n") ; od: # _R. J. Mathar_, Oct 30 2009
%K nonn,tabf
%O 1,1
%A _Pierre CAMI_, Nov 06 2003
%E Edited by _R. J. Mathar_, Oct 30 2009
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