This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140053 #8 Apr 04 2015 10:01:57
%S A140053 1,1,2,5,8,7,11,6,33,14,62,57,22,7,86,61,28,70,66,134,77,131,107,58,
%T A140053 161,252,240,52,155,32,152,322,167,200,284,258,28,173,95,563,369,57,
%U A140053 58,126,113,369
%N A140053 Indices k such that A114850(m)+A114850(k) is prime for some m>k.
%C A140053 The associated primes b(n), which grow too quickly for many to be given as a sequence themselves, are {primes of the form A114850(a) + A114850(b)} = {primes of the form A114850(a) + A114850(b)} and begin as follows. b(1) = 437893890380859631 = 256 + 437893890380859375 = 4^4 + 15^15 = semiprime(1)^semiprime(1) + semiprime(6)^semiprime(6).
%C A140053 b(2) = 88817841970012523233890533447265881 = 256 + 88817841970012523233890533447265625 = 4^4 + 25^25 = semiprime(1)^semiprime(1) + semiprime(9)^semiprime(9).
%C A140053 b(3) = 46656 + 88817841970012523233890533447265625 = 6^6 + 24^25 = semiprime(2)^semiprime(2) + semiprime(9)^semiprime(9). This is to A068145 "Primes of the form a^a + b^b" as A001358 semiprimes is to A000040 primes; and as A114850 "(n-th semiprime)^(n-th semiprime)" is to A051674 "(n-th prime)^(n-th prime)."
%C A140053 _M. F. Hasler_ gave the present definition which allows us to list merely the indices, which in the 3 examples above, are [6, 1],[9, 1],[9, 2]. The first 13 [m,k] value pairs are (as found by _M. F. Hasler_ as an extension) are [6, 1], [9, 1], [9, 2], [19, 5], [20, 8], [25, 7], [33, 11], [38, 6], [40, 33], [59, 14], [69, 62], [76, 57], [99, 22]. Hence our sequence begins a(1) = 6, a(2) = 9, a(3) = 9. For the sequence of corresponding k values {6, 9, 9, 19, 20, ...}, see A140052.
%F A140053 A001358(a(n))^A001358(a(n)) + A001358(A140052(n))^A001358(A140052(n)) is prime.
%e A140053 a(1) = 1 because semiprime(6)^semiprime(6) + semiprime(1)^semiprime(1) = 15^15 + 4^4 = 437893890380859375 + 256 = 437893890380859631 is prime.
%p A140053 ? t=0;A001358=vector(100,i,until(bigomega(t++)==2,);t); ? for(i=1,#A001358, for(j=1,i-1, ispseudoprime(A001358[i]^A001358[i]+A001358[j]^A001358[j]) | next; print1([i,j]",")))
%Y A140053 Cf. A000040, A001358, A051674, A068145, A114850, A137701, A140052.
%K A140053 more,nonn
%O A140053 1,3
%A A140053 _Jonathan Vos Post_, May 03 2008
%E A140053 a(14)-a(46) from _Donovan Johnson_, Nov 11 2008