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

5, 577, 5772156649015328606065120900824024310421

Offset

1,1

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

Links

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

Eric Weisstein's World of Mathematics, Constant Primes

Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant Digits

Index entries related to "constant primes".

Example

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

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 *)

Prog

(PARI) default(realprecision, 777); /* use that many digits */
A072952={(c=gamma, 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

Crossrefs

Cf. A005042 (analog for Pi), A007512 (analog for e), A119343 (analog for sqrt(3)).

Sequence in context: A299605 A185555 A093941 * A179634 A302379 A303100

Adjacent sequences: A072949 A072950 A072951 * A072953 A072954 A072955

Keyword

nonn,bref,base

Author

Shyam Sunder Gupta, Aug 12 2002

Status

approved