1,1

The sum of the reciprocals of this sequence converges to 0.7396851122524925502336739393520365903181567881168249430867370286656387769452467108115034824444490782... The Pari program below for powerpp(60) and powerpp(70) give this result for 100 digits. Is this number irrational? Transcendental? - Cino Hilliard (hillcino368(AT)gmail.com), Dec 14 2002

T. D. Noe, Table of n, a(n) for n=1..38

257 = 4^4 + 1^1 is a prime. 823799 = 4^4 + 7^7 is a prime.

k := 1; for i from 2 to 100 do for j from 1 to i-1 do a := i^i+j^j; if(isprime(a)=true) then feld[k] := a; k := k+1; end if; end do; end do; sort([seq(feld[p], p=1..k-1)]);

Select[ Union[ Flatten[ Table[a^a + b^b, {a, 1, 40}, {b, 1, a} ]]], PrimeQ ]

(PARI) powerpp(n) = { ct=0; sr=0; a=vector(n*n*n); for(x=1, n, for(y=x, n, v = x^x+y^y; if(isprime(v), ct+=1; a[ct] = v; \ print(x" "y" "z" "v" "ct); ); ); ); for(j=1, ct, for(k=j+1, ct, if(a[j] > a[k], tmp=a[k]; a[k]=a[j]; a[j]=tmp); ); ); for(j=1, ct, if(a[j]<>a[j+1], sr+=1.0/a[j]; print1(a[j]" ")); ); print(); print(sr); }

Adjacent sequences: A068142 A068143 A068144 this_sequence A068146 A068147 A068148

Sequence in context: A107389 A077483 A119242 this_sequence A032112 A058009 A097396

easy,nonn,nice

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 23 2002

Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com) and Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 01 2002