A221218 Let sequence B_n={b_m} be defined by: b_1=prime(n), b_2=prime(n+1); for m>=3, b_m=b_(m-2)+b_(m-1) if b_(m-2)+b_(m-1) is not semiprime, otherwise b_m is the least prime divisor of b_(m-2)+b_(m-1). Then a(n) is the maximal term of sequence B_n, or a(n)=0 if B_n is unbounded.

570, 570, 570, 570, 19726, 113750, 570, 22534, 570, 570, 570, 570, 399610, 570, 570, 570, 3138, 670, 570, 570, 772, 570, 570, 2448, 109472, 570, 570, 570, 1150, 609, 18644, 71049, 2276, 570, 1634, 1552, 13844, 798, 68830, 6940, 575, 1498, 668, 2551, 1586, 29729, 1748, 113750, 19726, 1435, 194650, 64360, 3213, 953988, 9146, 16539, 811, 8370238, 516878, 881, 99942, 7399, 4160, 215843, 8397, 676, 13397, 1715, 915722, 702, 3572, 141759, 1192, 1131, 762, 24895, 1194, 22534, 1750, 7069, 68830

Offset: 1

Author

Vladimir Shevelev, Feb 22 2013

Keywords

• nonn

Comments

Conjecture: All a(n)>=570. Conjecture: All sequences B_n are eventually periodic.

Moreover, our first observations show that up to n=8, the lengths of the periods is 36.

Peter J. C. Moses extended these observations and confirmed the same length 36 of all periods up to n=209.

Examples

			In case n=1, B_1 essentially coincides with A214156 and thus a(1)=570 which is the maximal term of A214156.
		

Crossrefs

Cf. A214156.

Extensions

Terms beginning with a(5) from Peter J. C. Moses