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Numbers n such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 9-less.
2

%I #7 Oct 14 2019 14:22:16

%S 1,2,3,4,5,11,13,15,26,27,33,36,48,51,55,60,61,65,71,83,100,101,106,

%T 112,115,116,117,123,126,151,170,173,177,200,203,206,216,221,225,230,

%U 231,233,234,235,240,241,253,255,271,275,281,283,284,286,287

%N Numbers n such that n, p[n], p[n]+n, p[n]-n and p[n]*n all are 9-less.

%C n, p[n], p[n]+n, p[n]-n and p[n]*n all are 0-less gives A104419.

%H Harvey P. Dale, <a href="/A104420/b104420.txt">Table of n, a(n) for n = 1..1000</a>

%t id[x_]:=IntegerDigits[x];pr[i_]:=Prime[i];ra=Range[300];A104420=Select[ra, Last[Union[id[ # ], id[pr[ # ]], id[pr[ # ]+# ], id[pr[ # ]-# ], id[pr[ # ]*# ]]]!=9&]

%t nlsQ[n_]:=Module[{p=Prime[n]},Max[DigitCount[{n,p,p+n,p-n,p*n},10,9]] == 0]; Select[Range[300],nlsQ] (* _Harvey P. Dale_, Oct 14 2019 *)

%Y Cf. A104419.

%K nonn,base

%O 1,2

%A _Zak Seidov_, Mar 07 2005