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

1,1

Links

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

Example

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

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));

Crossrefs

Cf. A002522, A225103, A246547.

Sequence in context: A094335 A300165 A316351 * A369957 A052231 A092178

Adjacent sequences: A282630 A282631 A282632 * A282634 A282635 A282636

Keyword

nonn

Author

Robert Israel and Altug Alkan, Feb 19 2017

Status

approved