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Primes formed by initial digits of 3^(1/3) = A002581, i.e., of the form floor[3^(1/3)*10^k].
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%I #21 Mar 30 2024 09:21:27

%S 144224957030740838232163,

%T 144224957030740838232163831078010958839186925349935057754641619454168759682999733

%N Primes formed by initial digits of 3^(1/3) = A002581, i.e., of the form floor[3^(1/3)*10^k].

%C Inspired by prime curios about 4957 (cf. LINKS), one of which honors the late Bruce Murray, 30.11.1931 - 29.8.2013.

%C See A210706 for the k-values. The keyword "less" for this records means that the next term (2488 digits) cannot be added / displayed here, and instead of listing further primes here, the k-values should be recorded in A210706.

%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) = floor[A002581 * 10^A210706(n)], where A002581 is taken as a constant.

%t With[{cr3=RealDigits[CubeRoot[3],10,100][[1]]},Select[Table[FromDigits[Take[cr3,n]],{n,100}],PrimeQ]] (* _Harvey P. Dale_, Mar 30 2024 *)

%o (PARI) (c=sqrtn(3,3),v=1/*set to 0 for indices instead of values*/)->for(k=0,precision(c),ispseudoprime(p=c\.1^k)&&print1([k,p][1+v]","))

%Y Cf. A005042 (analog for Pi), A007512 (analog for e), A115453 (analog for sqrt(2)), A119343 (analog for sqrt(3)), A072952 (analog for gamma).

%K nonn,bref,less,base

%O 1,1

%A _M. F. Hasler_, Aug 31 2013