A347904 Array read by antidiagonals, m, n >= 1: T(m,n) is 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, 3, 3, 7, 0, 5, 5, 5, 5, 5, 11, 0, 0, 0, 7, 7, 7, 7, 7, 7, 7, 23, 0, 13, 0, 11, 0, 17, 17, 41, 0, 23, 13, 0, 11, 19, 19, 0, 17, 0, 0, 0, 13, 0, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 23, 0, 0, 0, 19, 0, 17, 0, 0, 0, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13
Offset: 1
Examples
Array begins: m\n| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ---+--------------------------------------------------- 1 | 2 3 7 5 11 7 23 17 19 11 23 13 41 29 31 17 2 | 3 0 5 0 7 0 41 0 11 0 13 0 43 0 17 0 3 | 5 5 0 7 13 0 17 11 0 13 103 0 29 17 0 19 4 | 5 0 7 0 23 0 11 0 13 0 41 0 17 0 19 0 5 | 7 7 11 13 0 11 19 13 23 0 43 17 31 19 0 37 6 | 7 0 0 0 11 0 13 0 0 0 17 0 19 0 0 0 7 | 17 11 13 11 17 13 0 23 41 17 29 19 53 0 37 23 8 | 19 0 11 0 13 0 37 0 17 0 19 0 89 0 23 0 9 | 11 11 0 13 19 0 23 17 0 19 31 0 149 23 0 41 10 | 11 0 13 0 0 0 17 0 19 0 53 0 23 0 0 0 11 | 13 13 17 19 37 17 43 19 29 31 0 23 37 103 41 43 12 | 13 0 0 0 17 0 19 0 0 0 23 0 101 0 0 0 13 | 29 17 19 17 23 19 47 29 31 23 59 37 0 41 43 29 14 | 31 0 17 0 19 0 0 0 23 0 61 0 67 0 29 0 15 | 17 17 0 19 0 0 29 23 0 0 37 0 41 29 0 31 16 | 17 0 19 0 47 0 23 0 59 0 103 0 29 0 31 0 T(2,7) = 41, because the first prime in A022113, excluding the two initial terms, is 41.
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 A347904(m,n): if gcd(m,n) != 1: return 0 m,n = n,m+n while not isprime(n): m,n = n,m+n return n
Formula
T(m,n) = 0 if m and n have a common factor.
T(m,n) = T(n,m+n) if m+n is not prime, otherwise T(m,n) = m+n.
Comments