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

1,1

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

Table of n, a(n) for n=1..2.

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

Formula

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

Mathematica

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

Prog

(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]", "))

Crossrefs

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

Sequence in context: A340397 A094232 A234594 * A132185 A003942 A003935

Adjacent sequences: A210701 A210702 A210703 * A210705 A210706 A210707

Keyword

nonn,bref,less,base

Author

M. F. Hasler, Aug 31 2013

Status

approved