A385959 a(0) = 1; a(n) = a(n-1)*(b(n)+1)/(b(n)-1), where b(n) = A385958(n) is the largest prime p such that a(n) is an integer.

1, 2, 3, 4, 6, 7, 14, 15, 16, 18, 19, 38, 57, 76, 114, 115, 120, 121, 132, 135, 136, 138, 139, 278, 279, 310, 312, 314, 471, 628, 942, 1099, 2198, 2199, 2932, 4398, 5131, 10262, 10995, 10996, 16494, 19243, 38486, 41235, 41236, 41358, 41471, 41838, 41841, 46490, 55788, 55789, 111578, 167367, 168554, 252831, 252832, 252864

Offset: 0

Author

Thomas Ordowski, Jul 13 2025

Keywords

• nonn
• look

Comments

a(0) = 1; a(n) is the smallest k such that (k + a(n-1))/(k - a(n-1)) is a prime (A385958).

Note that a(n-1)+1 <= a(n) <= 2*a(n-1).

Links

• Martin Fuller, Table of n, a(n) for n = 0..3460

Crossrefs

Cf. A385958.

Formula

a(n) = Product_{k=1..n} (b(k)+1)/(b(k)-1), where b(n) = A385958(n).

a(n) = (1+t(n))/(1-t(n)) with t(n) = tanh(Sum_{k=1..n} arctanh(1/b(k))).

Extensions

More terms from Morné Louw and Martin Fuller, Jul 15 2025