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 A068145 Primes of the form a^a + b^b where a and b are positive integers. 12
 2, 5, 31, 257, 283, 823547, 823799, 10000823543, 11112006825558043, 437893890380859631, 39346408075296538398967, 20880467999847912043271133358823, 88817841970012523233890533447265881 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sum of the reciprocals of this sequence converges to 0.73968511225249255023367393935203659031815678811682494308673702866... The PARI program below for powerpp(60) and powerpp(70) give this result for 100 digits. Is this number irrational? Transcendental? - Cino Hilliard, Dec 14 2002 Note that 3 is also a prime of the form a^a + b^b where a = 2 and b = -1. But this sequence focuses on the positive values of a and b. - Altug Alkan, Jan 08 2016 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..94 EXAMPLE 257 = 4^4 + 1^1 is a prime. 823799 = 4^4 + 7^7 is a prime. MAPLE 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)]); MATHEMATICA nn=100; Select[ Union[ Flatten[ Table[a^a + b^b, {a, nn}, {b, a} ]]], # 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); } (PARI) v=[2]; for(a=2, 380, forstep(b=a%2+1, a-1, 2, if(ispseudoprime(t=a^a+b^b), v=concat(v, t); print(a"^"a" + "b"^"b)))); v \\ Charles R Greathouse IV, Feb 14 2011 CROSSREFS Sequence in context: A189559 A077483 A119242 * A032112 A058009 A056187 Adjacent sequences:  A068142 A068143 A068144 * A068146 A068147 A068148 KEYWORD nonn,nice AUTHOR Amarnath Murthy, Feb 23 2002 EXTENSIONS Edited and extended by Robert G. Wilson v and Sascha Kurz, Mar 01 2002 Name clarified by Altug Alkan, Jan 08 2016 STATUS approved

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Last modified June 24 12:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)