A210706 - OEIS

%I #22 Apr 03 2023 10:36:13

%S 23,80,2487

%N Numbers k such that floor[ 3^(1/3)*10^k ] is prime.

%C Inspired by prime curios about 4957 (cf. LINKS), one of which honors the late Bruce Murray (Nov 30 1931 - Aug 29 2013).

%C Meant to be a "condensed" version of A210704, see there for more.

%C Alternate definition: Numbers k such that concatenation of the first (k+1) digits of A002581 yields a prime.

%H C. Caldwell, G. L. Honaker (Eds.), <a href="https://t5k.org/curios/page.php?short=4957">4957 (another Prime Pages' Curiosity)</a>.

%F a(n) = (length of A210704(n)) - 1, where "length" means number of decimal digits.

%e t = 3^(1/3) = 1.44224957030740838232163831... multiplied by 10^23 yields

%e t*10^23 = 144224957030740838232163.831..., the integer part of which is the prime A210704(1), therefore a(1)=23.

%o (PARI) \p2999

%o t=sqrtn(3,3);for(i=1,2999,ispseudoprime(t\.1^i)&print1(i","))

%Y Cf. A002581 = decimal expansion of 3^(1/3).

%Y Cf. A065815 (analog for gamma), A060421 (1+ analog for Pi), A064118 (1+ analog for exp(1)), A119344 (1 + analog for sqrt(3)), A136583 (1+ analog for sqrt(10)).

%K nonn,base,more,bref

%O 1,1

%A _M. F. Hasler_, Aug 31 2013