A282633 Numbers n such that n^2 + 1 is the sum of two proper prime powers (A246547) in more than one way.

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

Offset: 1

Author

Robert Israel and Altug Alkan, Feb 19 2017

Keywords

• nonn

Examples

			83 is a term because 83^2 + 1 = 7^4 + 67^2 = 43^2 + 71^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2672

Crossrefs

Cf. A002522, A225103, A246547.

Programs

Maple

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));