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

23, 80, 2487

Offset: 1

Author

M. F. Hasler, Aug 31 2013

Keywords

• nonn
• base
• more
• bref

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.

Examples

			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.
		

Links

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

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)).

Programs

PARI

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

Formula

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