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A372627 Array read by antidiagonals. Row m consists of numbers k such that the sum of 2*m-1 primes starting at prime(k) is prime.

%I A372627 #12 May 11 2024 21:32:21
%S A372627 1,2,3,3,4,3,4,5,4,7,5,7,5,8,2,6,8,6,9,10,3,7,9,8,10,11,4,10,8,10,10,
%T A372627 11,12,5,13,2,9,11,11,14,15,6,15,4,2,10,13,14,15,22,8,18,8,3,5,11,16,
%U A372627 16,16,23,9,20,9,9,7,4,12,18,17,18,24,12,24,10,10,8,7,4,13,19,19,20,28,13,25
%N A372627 Array read by antidiagonals. Row m consists of numbers k such that the sum of 2*m-1 primes starting at prime(k) is prime.
%H A372627 Robert Israel, <a href="/A372627/b372627.txt">Table of n, a(n) for n = 1..10011</a> (first 141 antidiagonals, flattened)
%e A372627 Array starts
%e A372627  1   2   3   4   5   6   7   8   9  10
%e A372627  3   4   5   7   8   9  10  11  13  16
%e A372627  3   4   5   6   8  10  11  14  16  17
%e A372627  7   8   9  10  11  14  15  16  18  20
%e A372627  2  10  11  12  15  22  23  24  28  29
%e A372627  3   4   5   6   8   9  12  13  17  26
%e A372627 10  13  15  18  20  24  25  27  28  32
%e A372627  2   4   8   9  10  19  20  21  24  25
%e A372627  2   3   9  10  13  15  16  17  24  27
%e A372627  5   7   8   9  12  13  14  18  19  20
%e A372627 T(3,3) = 5 is a term because the sum of the 2*3 - 1 = 5 primes starting at prime(5) = 11 is 11 + 13 + 17 + 19 + 23 = 83, which is prime.
%p A372627 P:= select(isprime,[2,seq(i,i=3..10^6,2)]):
%p A372627 SP:= ListTools:-PartialSums(P):
%p A372627 A:= Matrix(20,20): A[1,1]:= 1:
%p A372627 for m from 1 to 20 do
%p A372627   if m = 1 then count:= 1 else count:= 0 fi;
%p A372627   for k from 1 while count < 20 do
%p A372627     if isprime(SP[k+2*m-1]-SP[k]) then
%p A372627       count:= count+1; A[m,count]:= k+1 fi
%p A372627 od od:
%p A372627 [seq(seq(A[i,m-i],i=1..m-1),m=2..21)];
%Y A372627 Cf. A215235 (1st column).
%K A372627 nonn,tabl
%O A372627 1,2
%A A372627 _Zak Seidov_ and _Robert Israel_, May 07 2024