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A094289 Decimal expansion of Sum(1/p^p) where p is prime. 11

%I #34 Feb 18 2024 08:26:14

%S 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,

%T 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,

%U 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

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

%C This constant approximately equals 5226294/18187381. - _Yalcin Aktar_, Nov 05 2006

%C The asymptotic mean of A129251. - _Amiram Eldar_, Nov 07 2022

%e 0.287358251306224179736418045878932206955908802685881709299499368947089...

%t 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 *)

%o (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]),",")) }

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

%K nonn,cons

%O 0,1

%A _Cino Hilliard_, Jul 31 2004

%E Offset corrected by _R. J. Mathar_, Feb 05 2009

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)