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A282633
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Numbers n such that n^2 + 1 is the sum of two proper prime powers (A246547) in more than one way.
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1
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47, 73, 83, 133, 157, 173, 187, 191, 203, 217, 317, 319, 353, 437, 463, 467, 487, 499, 557, 577, 583, 593, 599, 613, 623, 697, 703, 727, 733, 767, 829, 857, 863, 871, 931, 983, 1013, 1027, 1033, 1067, 1087, 1097, 1123, 1139, 1177, 1267, 1279, 1321, 1327, 1333, 1363, 1403, 1409, 1433, 1453, 1477, 1487, 1493, 1507, 1517, 1543, 1567, 1603, 1607, 1613
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OFFSET
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1,1
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LINKS
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EXAMPLE
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83 is a term because 83^2 + 1 = 7^4 + 67^2 = 43^2 + 71^2.
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MAPLE
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N:= 10^8: # to get all terms <= sqrt(N-1).
PP:= sort([seq(seq(p^k, k=2..floor(log[p](N))), p = select(isprime, [2, seq(i, i=3..floor(sqrt(N)), 2)]))]):
npp:= nops(PP):
res:= {}: R:= 'R':
for i from 2 to npp do
for j from 1 to i-1 do
q:= PP[i]+PP[j];
if q > N then break fi;
if issqr(q-1) then
if assigned(R[q]) then res:= res union {q}
else R[q]:= 1
fi fi
od od:
sort(convert(map(t -> sqrt(t-1), res), list));
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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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