%I #23 Apr 02 2017 02:05:30
%S 2,3,5,13,17,30,29,31,60,59,61,120,113,127,240,239,241,480,953,967,
%T 1920,3833,3847,7680,15359,15361,30720,30713,30727,61440,368633,
%U 368647,737280,737279,737281,1474560,16220143,16220177,32440320,32440319,32440321,64880640,194641919
%N Three-column array read by rows: the first row consists of the first two primes, p = 2 and q = 3, and their sum s = p + q = 5; afterwards the (n+1)-st row consists of the smallest pair of consecutive primes whose sum is a multiple of the sum in the n-th row followed by their sum.
%C Values of k (ratio of consecutive sums): 6, 2, 2, 2, 2, 4, 4, 4, 2, 12, 2, 22, 2, 6, 5, 5, 20, 4, 12, 15, 22, 27, 8, 13, 20, 5, 12, 28, 22, 55, 3, 8, 29, 12, 18, 6, 39, 22, 11, 34, 3, 162, 24, 4, 25, 15, 7, 4, 6, 10.
%C Values of p (1st column): 2, 13, 29, 59, 113, 239, 953, 3833, 15359, 30713, 368633, 737279, 16220143, 32440319, 194641919, 973209577, 4866047987, 97320959993, 389283839993, 4671406079947, 70071091199959, 1541564006399999, 41622228172799993, 332977825382399987, 4328711729971199933, 86574234599423999983, 432871172997119999999, 5194454075965439999993, 145444714127032319999971, 3199783710794711039999977, 175988104093709107199999981
%e In the 2nd row, 13 + 17 = 30 = 6*5, then 29 + 31 = 60 = 2*30, 59 + 61 = 120 = 2*60, etc.
%K nonn,tabf
%O 1,1
%A _Zak Seidov_, Apr 01 2017