1,1

There are exactly 87 such numbers, no one of them being prime:

32043, 32286, 33144, 35172, 35337, 35757, 35853, 37176, 37905, 38772, 39147, 39336, 40545, 42744, 43902, 44016, 45567, 45624, 46587, 48852, 49314, 49353, 50706, 53976, 54918, 55446, 55524, 55581, 55626, 56532, 57321, 58413, 58455, 58554, 59403, 60984, 61575, 61866, 62679, 62961, 63051, 63129, 65634, 65637, 66105, 66276, 67677, 68763, 68781, 69513, 71433, 72621, 75759, 76047, 76182, 77346, 78072, 78453, 80361, 80445, 81222, 81945, 83919, 84648, 85353, 85743, 85803, 86073, 87639, 88623, 89079, 89145, 89355, 89523, 90144, 90153, 90198, 91248, 91605, 92214, 94695, 95154, 96702, 97779, 98055, 98802, 99066.

f1[n_, k_]:=RealDigits[n][[1, k]]; f2[n_]:=RealDigits[n][[2]]; f3[n_]:=Module[{i=a0=a1=a2=a3=a4=a5=a6=a7=a8=a9=0}, Do[If[f1[n, i]==0, a0++ ]; If[f1[n, i]==1, a1++ ]; If[f1[n, i]==2, a2++ ]; If[f1[n, i]==3, a3++ ]; If[f1[n, i]==4, a4++ ]; If[f1[n, i]==5, a5++ ]; If[f1[n, i]==6, a6++ ]; If[f1[n, i]==7, a7++ ]; If[f1[n, i]==8, a8++ ]; If[f1[n, i]==9, a9++ ], {i, f2[n]}]; If[a0==1&&a0==a1&&a1==a2&&a2==a3&&a3==a4&&a4==a5&&a5==a6&&a6==a7&&a7==a8&&a8==a9\ , i=1, i=0]; i]; lst={}; Do[n=k^2; If[f2[n]>10, Break[]]; If[f2[n]==10, If[f3[n]==1, (*Print[n]; *)AppendTo[lst, k]]], {k, Floor[Sqrt[1023456789]], 120000}]; Print[lst, Length[lst]] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 22 2009]

A054038.

Sequence in context: A140939 A134124 A054038 this_sequence A097282 A146896 A137837

Adjacent sequences: A156974 A156975 A156976 this_sequence A156978 A156979 A156980

fini,full,nonn,base

Zak Seidov (zakseidov(AT)yahoo.com), Feb 20 2009