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A207890 a(0)=1; for n>=1,- the minimal increasing sequence, such that, for n>=1, the row sums of Pascal-like triangle with left side {1,1,1,...} and right side {a(0), a(1), a(2),...} form an increasing sequence of primes.

%I A207890 #15 May 01 2014 02:44:24
%S A207890 1,1,2,3,4,5,8,11,14,17,20,29,44,55,66,69,72,77,86,149,152,167,172,
%T A207890 183,198,229,230,233,254,267,276,285,316,355,370,377,402,423,458,469,
%U A207890 478,517,570,623,704,725,730,753,762,801,818,839,858,861,938,943,982
%N A207890 a(0)=1; for n>=1,- the minimal increasing sequence, such that, for n>=1, the row sums of Pascal-like triangle with left side {1,1,1,...} and right side {a(0), a(1), a(2),...} form an increasing sequence of primes.
%e A207890 Triangle begins
%e A207890 n/k.|..0.....1.....2.....3.....4.....5.....6.....7
%e A207890 ==================================================
%e A207890 .0..|..1
%e A207890 .1..|..1.....1
%e A207890 .2..|..1.....2.....2
%e A207890 .3..|..1.....3.....4.....3
%e A207890 .4..|..1.....4.....7.....7.....4
%e A207890 .5..|..1.....5....11....14....11.....5
%e A207890 .6..|..1.....6....16....25....25....16.....8
%e A207890 .7..|..1.....7....22....41....50....41....24.....11
%e A207890 .8..|
%e A207890 The row sums for n >= 1 form sequence A055496.
%t A207890 rows={{1},{1,1}}; Table[(x=Flatten[{1,2 MovingAverage[rows[[n]],2]}]; sx=Apply[Plus,x]; z=NextPrime[sx,NestWhile[#+1&,1,NextPrime[sx,#]-sx<Last[rows[[n]]]&]]-sx; rows=Append[rows,Append[x,z]]),{n,2,100}]; A207890=Map[Last[#]&,rows]
%Y A207890 Cf. A055496.
%K A207890 nonn,tabl
%O A207890 0,3
%A A207890 _Vladimir Shevelev_ and _Peter J. C. Moses_, Feb 21 2012