OFFSET
1,3
COMMENTS
By definition, a(2n-1) + a(2n) = A005574(n+1), and a(2n-1) is the minimal solution where the pair (a(2n-1), a(2n)) are both in A005574. The above conjecture says such a pair always exists. - Jens Kruse Andersen, Aug 27 2014
LINKS
Michel Lagneau, Table of n, a(n) for n = 1..5000
EXAMPLE
The 3rd pair (2,4) is in the sequence because for m = 2,4 and 2+4 = 6 we obtain three primes 2^2+1 = 5, 4^2+1 = 17 and 6^2+1 = 37.
The 6th number above 1 in A005574 is 16 which can be written as 2+14 or 6+10 using a pair in A005574. 2 is the minimal number in a solution so the 6th pair is (a(11), a(12)) = (2, 14). - Jens Kruse Andersen, Aug 27 2014
MAPLE
with(numtheory):lst:={}:nn:=10000:
for i from 1 to nn do:
if type(i^2+1, prime)=true
then
lst:=lst union {i}:
else
fi:
od:
n1:=nops(lst):
for n from 1 to 50 do:
m:=lst[n]:ii:=0:
for u from 1 to n1 while(ii=0)do:
for v from u to n1 while(ii=0)do:
a:=lst[u]:b:=lst[v]:
if m=a+b
then
ii:=1: printf(`%d, `, a): printf(`%d, `, b):
else
fi:
od:
od:
od:
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 26 2014
STATUS
approved