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 A073412 Lesser of three consecutive nonsquare integers each of which is the sum of two squares. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) == 0 mod 8. - Zak Seidov, Jan 26 2013 Is this sequence the same as A064715? - Zak Seidov, Jan 26 2013 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 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MAPLE 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 MATHEMATICA 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]; Select[8 Range[10000], selQ] (* Jean-François Alcover, Jun 11 2020 *) PROG (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 CROSSREFS Cf. A000404,A000415, A001481, A064716. Sequence in context: A050498 A077535 A064716 * A250749 A019507 A303081 Adjacent sequences:  A073409 A073410 A073411 * A073413 A073414 A073415 KEYWORD nonn AUTHOR Jason Earls, Aug 23 2002 EXTENSIONS Edited by Robert Israel, Mar 05 2018 STATUS approved

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)