Primes that are sums of eighth powers of two distinct primes.
Jonathan Post
jvospost3 at gmail.com
Wed Aug 15 20:07:41 CEST 2007
PRE-NUMBERED NEW SEQUENCE A132260 FROM Jonathan Vos Post
%I A132260
%S A132260 13, 89, 137, 29, 107, 223, 37, 59, 127, 331, 113, 53, 101,
139, 389, 113, 223, 181, 103, 173, 491,
%N A132260 Array A[k,n] = n-th prime p such that 2^2^k + p^2^k is
prime, k>2, by antidiagonals.
%C A132260 These were computed by Ignacio Larrosa CaÃ±estro
<ilarrosa at mundo-r.com>, who cautions that some are only probable
primes. The k=3 row is A132216. The main diagonal is A132261.
The array begins:
.n.|...1....2....3....4....5....6...7...8...9..10...
k=3.|..13..137..223..331..389..491.563.647.701.773...
k=4.|..89..107..127..139..173..179.229.233.349.421...
k=5.|..29...59..101..103..109..181.199.379.769.881...
k=6.|..37...53..181..491..547..619.661.677.911.941...
k=7.|.113..223.5279.7517.8039.9833...
k=8.|.113.1223.1277.1993.2399.9349.9739...
%Y A132260 Cf. A000040, A001016, A050997, A120398, A122616, A130873,
A130555, A132214, A132215, A132216.
%O A132260 1,1
%K A132260 ,more,nonn,
%A A132260 Jonathan Vos Post (jvospost2 at yahoo.com), Aug 15 2007
RH
RA 192.20.225.32
and also
PRE-NUMBERED NEW SEQUENCE A132261 FROM Jonathan Vos Post
%I A132261
%S A132261 13, 107, 101, 491, 8039, 9349
%N A132261 Main diagonal of Array in A132260 A[k,n] = n-th prime p such
that 2^2^k + p^2^k is prime, k>2.
%C A132261 These were computed by Ignacio Larrosa CaÃ±estro
<ilarrosa at mundo-r.com>, who cautions that some are only probable
primes. The k=3 row is A132216. The array read by antidiagonals is A132260.
The array begins:
.n.|...1....2....3....4....5....6...7...8...9..10...
k=3.|..13..137..223..331..389..491.563.647.701.773...
k=4.|..89..107..127..139..173..179.229.233.349.421...
k=5.|..29...59..101..103..109..181.199.379.769.881...
k=6.|..37...53..181..491..547..619.661.677.911.941...
k=7.|.113..223.5279.7517.8039.9833...
k=8.|.113.1223.1277.1993.2399.9349.9739...
%F A132261 a(n) = A[n,n+2] = n-th prime p such that 2^2^(n+2) +
p^2^(n+2) is prime.
%e A132261 a(1) = 13 because 13 is the first prime p such that 2^2^3 +
p^2^3 is prime.
a(2) = 107 because 107 is the 2nd prime p such that 2^2^4 + p^2^4 is
prime.
a(3) = 101 because 101 is the 3rd prime p such that 2^2^5 + p^2^5 is
prime.
%Y A132261 Cf. A000040, A001016, A050997, A120398, A122616, A130873,
A130555, A132214, A132215, A132216, A132260.
%O A132261 1,1
%K A132261 ,more,nonn,
%A A132261 Jonathan Vos Post (jvospost2 at yahoo.com), Aug 15 2007
RH
RA 192.20.225.32
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