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A282633 Numbers n such that n^2 + 1 is the sum of two proper prime powers (A246547) in more than one way. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A052231 A092178 A165335

Adjacent sequences:  A282630 A282631 A282632 * A282634 A282635 A282636

KEYWORD

nonn

AUTHOR

Robert Israel and Altug Alkan, Feb 19 2017

STATUS

approved

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Last modified September 22 12:19 EDT 2019. Contains 327307 sequences. (Running on oeis4.)