A094289 Decimal expansion of Sum(1/p^p) where p is prime.

2, 8, 7, 3, 5, 8, 2, 5, 1, 3, 0, 6, 2, 2, 4, 1, 7, 9, 7, 3, 6, 4, 1, 8, 0, 4, 5, 8, 7, 8, 9, 3, 2, 2, 0, 6, 9, 5, 5, 9, 0, 8, 8, 0, 2, 6, 8, 5, 8, 8, 1, 7, 0, 9, 2, 9, 9, 4, 9, 9, 3, 6, 8, 9, 4, 7, 0, 8, 9, 3, 2, 9, 2, 7, 8, 6, 8, 8, 9, 3, 9, 7, 7, 0, 2, 0, 9, 1, 2, 4, 2, 8, 0, 0, 2, 9, 0, 9, 0, 0, 5, 5, 9, 2, 9

Offset: 0

Author

Cino Hilliard, Jul 31 2004

Keywords

• nonn
• cons

Comments

This constant approximately equals 5226294/18187381. - Yalcin Aktar, Nov 05 2006

The asymptotic mean of A129251. - Amiram Eldar, Nov 07 2022

Examples

			0.287358251306224179736418045878932206955908802685881709299499368947089...
		

Crossrefs

Cf. A073009, A083648, A051674 (prime(n)^prime(n)), A129251.

Programs

Mathematica

digits = 105; n0 = 10; dn = 10; Clear[f]; f[n_] := f[n] = RealDigits[ Sum[ 1/Prime[k]^Prime[k], {k, 1, n}], 10, digits+5] // First; f[n = n0]; f[n = n+dn]; While[Print["n = ", n]; f[n] != f[n-dn], n = n+dn]; Take[f[n], digits] (* Jean-François Alcover, Nov 22 2013 *)

PARI

ptothep(n) = { local(x,s,a); default(realprecision,200); s=0; forprime(x=2,n,s+=1./x^x); a=Vec(Str(s)); for(x=3,n,print1(eval(a[x]),",")) }

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009