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A174433
Triangle read by rows: T(n,k) = prime(n) mod A001223(k), where A001223 are differences between consecutive primes.
2
0, 0, 1, 0, 1, 1, 0, 1, 1, 3, 0, 1, 1, 3, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 3, 1, 3, 1, 3, 0, 1, 1, 3, 1, 3, 1, 3, 5, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 0, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 5, 1, 5, 1, 1, 0, 1, 1, 3, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3
OFFSET
1,10
COMMENTS
The first prime gap is 3-2=1, so the first column is T(n,1)=0. The second and third prime gaps are 5-3=2 and 7-5=2, and since all primes > 2 are odd, T(n,2) = T(n,3) = 1.
EXAMPLE
Triangle begins:
0;
0,1;
0,1,1;
0,1,1,3;
0,1,1,3,1;
MAPLE
A001223 := proc(n) ithprime(n+1)-ithprime(n) ; end proc:
A174433 := proc(n, k) ithprime(n) mod A001223(k) ; end proc:
seq(seq(A174433(n, k), k=1..n), n=1..14) ;
CROSSREFS
Cf. A000040.
Sequence in context: A350829 A249767 A341411 * A174624 A029358 A088512
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved