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%I #17 Nov 14 2023 13:10:46
%S 2,5,8,11,12,14,16,17,20,22,23,26,29,30,32,34,35,36,38,41,44,45,47,48,
%T 50,53,55,56,58,59,61,62,65,68,71,72,74,77,78,80,83,84,85,86,87,89,90,
%U 92,95,96,98,100,101,104,107,108,110,111,112,113,114,116,119,121,122
%N Numbers in which inserting, prefixing or suffixing a 1 anywhere yields only composite numbers.
%H Harvey P. Dale, <a href="/A070328/b070328.txt">Table of n, a(n) for n = 1..1000</a>
%e 26 is a member as the three numbers 126, 216 and 261 obtained by placing a 1 at all possible places are composite.
%p anz := 0:for i from 2 to 1500 do b := convert(i,base,10):s := sum(b[l],l=1..nops(b)): ok := true:for j from 0 to nops(b) do q := sum(b[k]*10^(k-1),k=1..j):q := q+10^(j): q := q+sum(b[k]*10^k,k=j+1..nops(b)): if(isprime(q)) then ok := false:fi:od: if(ok=true) then anz := anz+1:a[anz] := i:fi:od:seq(a[l],l=1..anz);
%t Select[Range[200],AllTrue[FromDigits/@Table[Insert[IntegerDigits[#],1,n],{n,IntegerLength[ #]+ 1}],CompositeQ]&] (* _Harvey P. Dale_, Nov 14 2023 *)
%Y Cf. A002808, A070329.
%K base,nonn
%O 1,1
%A _Amarnath Murthy_, May 11 2002
%E Corrected and extended by _Sascha Kurz_, Jan 26 2003