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%I #45 Jun 11 2020 16:52:08
%S 72,232,520,584,800,808,1096,1152,1312,1664,1744,1800,1872,1960,2248,
%T 2312,2384,2592,2824,3328,3392,3528,4112,4176,4328,5120,5408,5904,
%U 6056,6120,6272,6352,6408,6568,6920,8080,8144,8296,8352,8584,8712,9160,9376
%N Lesser of three consecutive nonsquare integers each of which is the sum of two squares.
%C a(n) == 0 mod 8. - _Zak Seidov_, Jan 26 2013
%C Is this sequence the same as A064715? - _Zak Seidov_, Jan 26 2013
%C 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
%C 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
%H Robert Israel, <a href="/A073412/b073412.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%e 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.
%p is415:= proc(n) local F;
%p if issqr(n) then return false fi;
%p F:= select(t -> t[1] mod 4 = 3, ifactors(n)[2]);
%p andmap(t -> t[2]::even, F);
%p end proc:
%p Q:= select(is415, [seq(seq(8*i+j,j=0..2),i=1..2000)]):
%p Q[select(t -> Q[t+2]-Q[t]=2, [$1..nops(Q)-2])]; # _Robert Israel_, Mar 05 2018
%t nsQ[x_] := !IntegerQ[Sqrt[x]];
%t prQ[x_] := With[{pr = PowersRepresentations[x, 2, 2]}, pr != {} && AllTrue[pr[[1]], IntegerQ]];
%t selQ[x_] := nsQ[x] && nsQ[x+1] && nsQ[x+2] && prQ[x] && prQ[x+1] && prQ[x+2];
%t Select[8 Range[10000], selQ] (* _Jean-François Alcover_, Jun 11 2020 *)
%o (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;
%o isok(n) = isA001481(n) && isA001481(n+1) && isA001481(n+2) && !issquare(n) && !issquare(n+1);
%o lista(nn) = for(n=1, nn, if(isok(8*n), print1(8*n, ", "))); \\ _Altug Alkan_, Jul 07 2016
%Y Cf. A000404,A000415, A001481, A064716.
%K nonn
%O 1,1
%A _Jason Earls_, Aug 23 2002
%E Edited by _Robert Israel_, Mar 05 2018
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