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A348598
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Least prime p of the form k^2+1 such that p == A002496(n) (mod A002496(n+1)) with p>A002496(n), or 0 if no such p exists.
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2
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17, 1297, 90001, 1008017, 147457, 2421137, 15952037, 1378277, 7203857, 107122501, 164968337, 34503877, 38688401, 4851958337, 1075577617, 197121601, 1044582401, 315559697, 70924211857, 730296577, 20705483237, 15103426817, 197740302401, 4587352901, 155964965777
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OFFSET
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1,1
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COMMENTS
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a(n) == 1, 5 (mod 16).
Conjecture: Consider the smallest prime p of the form k^2+1 such that p is congruent to A002496(n) modulo q, q prime of the form m^2+1 > A002496(n). Then q = A002496(n+1).
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LINKS
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EXAMPLE
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a(2) = 1297 because 1297 == A002496(2) (mod A002496(3)) => 1297 == 5 (mod 17).
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MAPLE
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with(numtheory):T:=array(1..30000):k:=0:
nn:=500000:
for m from 1 to nn do:
if isprime(m^2+1)
then
k:=k+1:T[k]:=m^2+1:
else
fi:
od:
for n from 1 to 32 do:
ii:=0:r:=T[n]:q:=T[n+1]:
for i from 1 to k while(ii=0) do:
p:=T[i]:r1:=irem(p, q):
if r1=r and p>q
then
ii:=1: printf(`%d, `, p)
else
fi:
od:
od:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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