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

1,2

Links

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

Example

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.

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)];

Crossrefs

Cf. A215235 (1st column).

Sequence in context: A179846 A086925 A088858 * A113312 A334954 A053475

Adjacent sequences: A372624 A372625 A372626 * A372628 A372629 A372631

Keyword

nonn,tabl

Author

Zak Seidov and Robert Israel, May 07 2024

Status

approved