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.

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, 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, 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

Offset: 1

Author

Zak Seidov and Robert Israel, May 07 2024

Keywords

• nonn
• tabl

Examples

			Array starts
 1   2   3   4   5   6   7   8   9  10
 3   4   5   7   8   9  10  11  13  16
 3   4   5   6   8  10  11  14  16  17
 7   8   9  10  11  14  15  16  18  20
 2  10  11  12  15  22  23  24  28  29
 3   4   5   6   8   9  12  13  17  26
10  13  15  18  20  24  25  27  28  32
 2   4   8   9  10  19  20  21  24  25
 2   3   9  10  13  15  16  17  24  27
 5   7   8   9  12  13  14  18  19  20
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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals, flattened)

Crossrefs

Cf. A215235 (1st column).

Programs

Maple

P:= select(isprime,[2,seq(i,i=3..10^6,2)]):
SP:= ListTools:-PartialSums(P):
A:= Matrix(20,20): A[1,1]:= 1:
for m from 1 to 20 do
  if m = 1 then count:= 1 else count:= 0 fi;
  for k from 1 while count < 20 do
    if isprime(SP[k+2*m-1]-SP[k]) then
      count:= count+1; A[m,count]:= k+1 fi
od od:
[seq(seq(A[i,m-i],i=1..m-1),m=2..21)];