A347905 Array read by antidiagonals, m, n >= 1: T(m,n) is the position of the first prime (after the two initial terms) in the Fibonacci-like sequence with initial terms m and n, or 0 if no such prime exists.
2, 2, 2, 3, 0, 3, 2, 2, 2, 2, 3, 0, 0, 0, 3, 2, 2, 2, 2, 2, 2, 4, 0, 3, 0, 3, 0, 4, 3, 5, 0, 4, 3, 0, 3, 4, 3, 0, 3, 0, 0, 0, 3, 0, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 0, 0, 0, 3, 0, 3, 0, 0, 0, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 0, 6, 0, 3, 0, 0, 0, 3, 0, 3, 0, 4
Offset: 1
Examples
Array begins: m\n| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ---+------------------------------------------------------------ 1 | 2 2 3 2 3 2 4 3 3 2 3 2 4 3 3 2 4 2 4 3 2 | 2 0 2 0 2 0 5 0 2 0 2 0 4 0 2 0 2 0 4 0 3 | 3 2 0 2 3 0 3 2 0 2 6 0 3 2 0 2 3 0 3 2 4 | 2 0 2 0 4 0 2 0 2 0 4 0 2 0 2 0 4 0 2 0 5 | 3 2 3 3 0 2 3 2 3 0 4 2 3 2 0 3 4 2 3 0 6 | 2 0 0 0 2 0 2 0 0 0 2 0 2 0 0 0 2 0 5 0 7 | 4 3 3 2 3 2 0 3 4 2 3 2 4 0 3 2 3 3 4 3 8 | 4 0 2 0 2 0 4 0 2 0 2 0 5 0 2 0 4 0 4 0 9 | 3 2 0 2 3 0 3 2 0 2 3 0 6 2 0 3 3 0 3 2 10 | 2 0 2 0 0 0 2 0 2 0 4 0 2 0 0 0 4 0 2 0 11 | 3 2 3 3 4 2 4 2 3 3 0 2 3 5 3 3 4 2 4 2 12 | 2 0 0 0 2 0 2 0 0 0 2 0 5 0 0 0 2 0 2 0 13 | 4 3 3 2 3 2 4 3 3 2 4 3 0 3 3 2 3 2 4 3 14 | 4 0 2 0 2 0 0 0 2 0 4 0 4 0 2 0 2 0 5 0 15 | 3 2 0 2 0 0 3 2 0 0 3 0 3 2 0 2 6 0 3 0 16 | 2 0 2 0 4 0 2 0 4 0 5 0 2 0 2 0 4 0 4 0 17 | 3 2 3 5 10 2 3 6 4 3 4 2 3 2 3 5 0 3 7 2 18 | 2 0 0 0 2 0 5 0 0 0 2 0 2 0 0 0 5 0 2 0 19 | 4 3 4 2 3 3 4 5 3 2 3 2 6 3 4 5 3 2 0 3 20 | 4 0 2 0 0 0 4 0 2 0 2 0 4 0 0 0 2 0 4 0 T(2,7) = 5, because 5 is the smallest k >= 2 for which A022113(k) is prime.
Programs
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Python
# Note that in the (rare) case when m and n are coprime but there are no primes in the Fibonacci-like sequence, this function will go into an infinite loop. from sympy import isprime,gcd def A347905(m,n): if gcd(m,n) != 1: return 0 m,n = n,m+n k=2 while not isprime(n): m,n = n,m+n k += 1 return k
Formula
T(m,n) = 0 if m and n have a common factor.
T(m,n) = T(n,m+n) + 1 if m+n is not prime, otherwise T(m,n) = 2.
Comments