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A073412
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Lesser of three consecutive nonsquare integers each of which is the sum of two squares.
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3
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72, 232, 520, 584, 800, 808, 1096, 1152, 1312, 1664, 1744, 1800, 1872, 1960, 2248, 2312, 2384, 2592, 2824, 3328, 3392, 3528, 4112, 4176, 4328, 5120, 5408, 5904, 6056, 6120, 6272, 6352, 6408, 6568, 6920, 8080, 8144, 8296, 8352, 8584, 8712, 9160, 9376
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OFFSET
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1,1
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COMMENTS
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This sequence is distinct from A064715 since it allows numbers equal to twice a square, like 72, 1152, 2592, 3528, etc. - Giovanni Resta, Jan 29 2013
This sequence lists lesser of three consecutive nonsquare integers each of which is the sum of two squares. So this sequence is a subsequence of A064716. - Altug Alkan, Jul 07 2016
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LINKS
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EXAMPLE
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232 is here since 232 = 6^2 + 14^2; 233 = 8^2 + 13^2; 234 = 3^2 + 15^2 and 232, 233, 234 are all nonsquares.
288 is not a term because 288 = 12^2 + 12^2, 289 = 8^2 + 15^2, 290 = 1^2 + 17^2 but 289 is also square.
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MAPLE
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is415:= proc(n) local F;
if issqr(n) then return false fi;
F:= select(t -> t[1] mod 4 = 3, ifactors(n)[2]);
andmap(t -> t[2]::even, F);
end proc:
Q:= select(is415, [seq(seq(8*i+j, j=0..2), i=1..2000)]):
Q[select(t -> Q[t+2]-Q[t]=2, [$1..nops(Q)-2])]; # Robert Israel, Mar 05 2018
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MATHEMATICA
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nsQ[x_] := !IntegerQ[Sqrt[x]];
prQ[x_] := With[{pr = PowersRepresentations[x, 2, 2]}, pr != {} && AllTrue[pr[[1]], IntegerQ]];
selQ[x_] := nsQ[x] && nsQ[x+1] && nsQ[x+2] && prQ[x] && prQ[x+1] && prQ[x+2];
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PROG
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(PARI) isA001481(n) = my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]%2 && f[i, 1]%4==3, return(0))); 1;
isok(n) = isA001481(n) && isA001481(n+1) && isA001481(n+2) && !issquare(n) && !issquare(n+1);
lista(nn) = for(n=1, nn, if(isok(8*n), print1(8*n, ", "))); \\ Altug Alkan, Jul 07 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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