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

1,1

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.

Links

Table of n, a(n) for n=1..81.

Example

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.

Sequence in context: A240715 A263708 A219992 * A252465 A252473 A252466

Adjacent sequences: A221215 A221216 A221217 * A221219 A221220 A221221

Keyword

nonn

Author

Vladimir Shevelev, Feb 22 2013

Extensions

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

Status

approved