A210706 Numbers k such that floor[ 3^(1/3)*10^k ] is prime.

23, 80, 2487

Offset

1,1

Comments

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

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

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

Links

Table of n, a(n) for n=1..3.

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

Formula

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

Example

t = 3^(1/3) = 1.44224957030740838232163831... multiplied by 10^23 yields
t*10^23 = 144224957030740838232163.831..., the integer part of which is the prime A210704(1), therefore a(1)=23.

Prog

(PARI) \p2999
t=sqrtn(3, 3); for(i=1, 2999, ispseudoprime(t\.1^i)&print1(i", "))

Crossrefs

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

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)).

Sequence in context: A078597 A280576 A160297 * A304592 A302729 A139940

Adjacent sequences: A210703 A210704 A210705 * A210707 A210708 A210709

Keyword

nonn,base,more,bref

Author

M. F. Hasler, Aug 31 2013

Status

approved