OFFSET
0,1
COMMENTS
In order to get the next number in the row, you add the two numbers above it, and find the next prime.
3 is the only prime number that never shows up.
5 is the only prime number that only shows up once; every prime number above 5 shows up at least twice.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0..150, flattened)
FORMULA
T(n,k) = A007918(T(n-1,k-1) + T(n-1,k)) for 0 < k < n. - Robert Israel, Apr 05 2023
EXAMPLE
Triangle begins:
k=0 1 2 3 4 5 6 7 8 9 10
n=0: 2
n=1: 2 2
n=2: 2 5 2
n=3: 2 7 7 2
n=4: 2 11 17 11 2
n=5: 2 13 29 29 13 2
n=6: 2 17 43 59 43 17 2
n=7: 2 19 61 103 103 61 19 2
n=8: 2 23 83 167 211 167 83 23 2
n=9: 2 29 107 251 379 379 251 107 29 2
n=10: 2 31 137 359 631 761 631 359 137 31 2
MAPLE
for n from 0 to 10 do
T[n, 0]:= 2: T[n, n]:= 2:
for k from 1 to n-1 do
T[n, k]:= nextprime(T[n-1, k-1]+T[n-1, k]-1)
od
od:
for n from 0 to 10 do
seq(T[n, k], k=0..n)
od; # Robert Israel, Apr 05 2023
MATHEMATICA
T[n_, 0] := T[n, n] = 2; T[n_, k_] := T[n, k] = NextPrime[T[n - 1, k - 1] + T[n - 1, k] - 1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Apr 06 2023, after Maple *)
PROG
(PARI) T(n, k) = if (n==0, 2, if (k==0, 2, if (k==n, 2, nextprime(T(n-1, k-1) + T(n-1, k))))); \\ Michel Marcus, Apr 07 2023
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jack Braxton, Apr 05 2023
STATUS
approved