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Primes derived from A116516.
1

%I #9 Jun 04 2024 16:48:58

%S 2,7,37,263,2897,37663,640279,12165313,279802207,8114264027,

%T 251542184851,9307060839509,381589494419909,16408348260056111,

%U 771192368222637247,40873195515799774129,2411518535432186673637

%N Primes derived from A116516.

%C While calculating every possible C for such a sequence, the first "split" seems to be at C*193#, i.e. there appear to be two primes that simultaneously continue the sequence: floor[C*191# ]*193+30 and floor[C*191# ]*193+88. Terms above a(43) given here correspond to the smallest possible primes in the sequence. See also the arXiv paper linked below.

%H Martin Raab, <a href="/A125515/b125515.txt">Table of n, a(n) for n = 1..100</a>

%H Martin Raab, <a href="https://arxiv.org/abs/2403.17949">A prime number "Game of Life": can floor(y*p#) be prime for all p>=2?</a>, arXiv:2403.17949 [math.GM], 2024.

%F Floor[C*p# ] where C=1.254196101578...

%e a(5)=2897 because the fifth prime is 11 and floor[11#*1.2541961...] = 2897 (2310*1.2541961... = 2897.19299...).

%Y Cf. A116516.

%K nonn

%O 1,1

%A _Martin Raab_, Jan 21 2007, Feb 02 2007