A210704 Primes formed by initial digits of 3^(1/3) = A002581, i.e., of the form floor[3^(1/3)*10^k].

144224957030740838232163, 144224957030740838232163831078010958839186925349935057754641619454168759682999733

Offset: 1

Author

M. F. Hasler, Aug 31 2013

Keywords

• nonn
• bref
• less
• base

Comments

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

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.

Links

• C. Caldwell, G.L. Honaker (Eds.), 4957 (another Prime Pages' Curiosity).

Crossrefs

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

Programs

Mathematica

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

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]","))

Formula

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