A231608 - OEIS

%I #17 Nov 19 2014 14:26:24

%S 3,3,5,5,7,11,3,7,13,17,3,5,11,19,29,5,7,11,13,37,41,3,7,13,23,17,43,

%T 59,3,5,11,19,29,23,67,71,5,7,17,17,31,53,31,79,101,3,11,13,23,19,37,

%U 59,37,97,107,7,11,13,31,29,29,43,71,41,103,137

%N Table whose n-th row consists of primes p such that p + 2n is also prime, read by antidiagonals.

%H T. D. Noe, <a href="/A231608/b231608.txt">Rows n = 1..100 of triangle, flattened</a>

%e The following sequences are read by antidiagonals

%e {3, 5, 11, 17, 29, 41, 59, 71, 101, 107,...}

%e {3, 7, 13, 19, 37, 43, 67, 79, 97, 103,...}

%e {5, 7, 11, 13, 17, 23, 31, 37, 41, 47,...}

%e {3, 5, 11, 23, 29, 53, 59, 71, 89, 101,...}

%e {3, 7, 13, 19, 31, 37, 43, 61, 73, 79,...}

%e {5, 7, 11, 17, 19, 29, 31, 41, 47, 59,...}

%e {3, 5, 17, 23, 29, 47, 53, 59, 83, 89,...}

%e {3, 7, 13, 31, 37, 43, 67, 73, 97, 151,...}

%e {5, 11, 13, 19, 23, 29, 41, 43, 53, 61,...}

%e {3, 11, 17, 23, 41, 47, 53, 59, 83, 89,...}

%e ...

%p A231608 := proc(n,k)

%p     local j,p ;

%p     j := 0 ;

%p     p := 2;

%p     while j < k do

%p         if isprime(p+2*n ) then

%p             j := j+1 ;

%p         end if;

%p         if j = k then

%p             return p;

%p         end if;

%p         p := nextprime(p) ;

%p     end do:

%p end proc:

%p for n from 1 to 10 do

%p     for k from 1 to 10 do

%p         printf("%3d ",A231608(n,k)) ;

%p     end do;

%p     printf("\n") ;

%p end do: # _R. J. Mathar_, Nov 19 2014

%t nn = 10; t = Table[Select[Range[100*nn], PrimeQ[#] && PrimeQ[# + 2*n] &, nn], {n, nn}]; Table[t[[n-j+1, j]], {n, nn}, {j, n}]

%Y Cf. A001359, A023200, A023201, A023202, A023203.

%Y Cf. A046133, A153417, A049488, A153418, A153419.

%Y Cf. A020483 (numbers in first column).

%Y Cf. A086505 (numbers on the diagonal).

%K nonn,tabl

%O 1,1

%A _T. D. Noe_, Nov 26 2013