A072952 Primes obtained as initial segments of the decimal expansion of the Euler-Mascheroni constant gamma = 0.5772... .

5, 577, 5772156649015328606065120900824024310421

Offset: 1

Author

Shyam Sunder Gupta, Aug 12 2002

Keywords

• nonn
• base

Comments

The next term (a(4)) has 185 digits and is too large to include. - Harvey P. Dale, May 14 2013

Sequence A065815 gives the number of digits of a(n), resp. numbers k such that a(n) = floor(gamma*10^k). Sequences A005042, A007512, A115453, A119343, A210704, ... are the analog of the present sequence for Pi, e, sqrt(2), sqrt(3), 3^(1/3), ... - M. F. Hasler, Aug 31 2013

The original wording of the definition (and example) was "primes found in the decimal expansion..." which could as well refer to the sequence (5,7,7,215664901,5,3,2, ...) or (5,7,72156649, ...) or (5,7,7215664901, ...) (analogs to A047777 or A195834), or to the sequence (5,7,57, ...), analog to A198018. - M. F. Hasler, Sep 01 2013

Examples

			a(2) = 577, since 577 is the second prime obtained as initial segment of the decimal expansion of Euler-Mascheroni constant gamma = 0.577215664... .
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4
• Eric Weisstein's World of Mathematics, Constant Primes.
• Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant Digits.
• Index entries related to "constant primes".

Crossrefs

Cf. A001620, A047777, A065815, A195834, A198018.

Analogous sequences: A005042 (Pi), A007512 (e), A115453 (sqrt(2)), A119343 (sqrt(3)), A210704 (3^(1/3)).

Programs

Mathematica

nn=200;With[{emc=RealDigits[EulerGamma,10,nn][[1]]},Select[Table[ FromDigits[ Take[emc,n]],{n,nn}],PrimeQ]] (* Harvey P. Dale, May 14 2013 *)

PARI

default(realprecision, 777); /* use that many digits */
A072952={(c=Euler, v=1/*set to 0 for indices (i.e., A065815) instead of values*/)->for(k=0, precision(c), ispseudoprime(p=c\.1^k)&&print1([k, p][1+v]", "))} \\ M. F. Hasler, Aug 31 2013