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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.
1
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
KEYWORD
nonn,tabl
AUTHOR
Zak Seidov and Robert Israel, May 07 2024
STATUS
approved