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Search: id:A140053
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| 1, 1, 2, 5, 8, 7, 11, 6, 33, 14, 62, 57, 22, 7, 86, 61, 28, 70, 66, 134, 77, 131, 107, 58, 161, 252, 240, 52, 155, 32, 152, 322, 167, 200, 284, 258, 28, 173, 95, 563, 369, 57, 58, 126, 113, 369
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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).
b(2) = 88817841970012523233890533447265881 = 256 + 88817841970012523233890533447265625 = 4^4 + 25^25 = semiprime(1)^semiprime(1) + semiprime(9)^semiprime(9).
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)."
Maximilian Hasler (maximilian.hasler(AT)gmail.com) 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 Maximilian 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.
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FORMULA
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A001358(a(n))^A001358(a(n)) + A001358(A140052(n))^A001358(A140052(n)) is prime.
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EXAMPLE
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a(1) = 1 because semiprime(6)^semiprime(6) + semiprime(1)^semiprime(1) = 15^15 + 4^4 = 437893890380859375 + 256 = 437893890380859631 is prime.
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MAPLE
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? 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]", ")))
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CROSSREFS
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Cf. A000040, A001358, A051674, A068145, A114850, A137701, A140052.
Sequence in context: A011201 A118119 A057929 this_sequence A103311 A019824 A019772
Adjacent sequences: A140050 A140051 A140052 this_sequence A140054 A140055 A140056
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KEYWORD
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more,nonn,new
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 03 2008
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EXTENSIONS
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a(14)-a(46) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 11 2008
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