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A181333 a(n) cannot be prefixed or followed by any digit to form a semiprime.

%I A181333 #18 Feb 03 2025 02:24:08
%S A181333 60,208,252,552,588,630,656,696,710,768,816,864,1025,1028,1050,1225,
%T A181333 1280,1300,1432,1804,1950,2004,2016,2152,2160,2376,2410,2664,2672,
%U A181333 2808,2920,2988,3172,3230,3356
%N A181333 a(n) cannot be prefixed or followed by any digit to form a semiprime.
%C A181333 Analogy: semiprimes A001358 are to primes A000040 as this sequence is to A032734.
%H A181333 Robert Israel, <a href="/A181333/b181333.txt">Table of n, a(n) for n = 1..10000</a>
%e A181333 a(1) = 60 because 60 (any digit to the left still gives a multiple of 10, not a semiprime) and
%e A181333 601 is prime,
%e A181333 602 = 2 * 7 * 43,
%e A181333 603 = 3^2 * 67,
%e A181333 604 = 2^2 * 151,
%e A181333 605 = 5 * 11^2,
%e A181333 606 = 2 * 3 * 101,
%e A181333 607 is prime,
%e A181333 608 = 2^5 * 19,
%e A181333 609 = 3 * 7 * 29.
%e A181333 a(2) = 208 because any digit to the left still ends in 8, and is nonsemiprime, and:
%e A181333 2081 is prime,
%e A181333 2082 = 2 * 3 * 347,
%e A181333 2083 is prime,
%e A181333 2084 = 2^2 * 521,
%e A181333 2085 = 3 * 5 * 139,
%e A181333 2086 = 2 * 7 * 149,
%e A181333 2087 is prime,
%e A181333 2088 = 2^3 *  3^2 * 29,
%e A181333 2089 is prime.
%p A181333 filter:= proc(n) local i,r; r:= 10^(1+ilog10(n)); not ormap(t -> numtheory:-bigomega(t)=2, [seq(i*r+n, i=1..9),seq(10*n+i,i=0..9)]) end proc:
%p A181333 select(filter, [$1..10000]); # _Robert Israel_, Feb 02 2025
%t A181333 fQ[n_] := Block[{d = Range[0, 9], id = IntegerDigits@ n}, Union[ semiPrimeQ@ # & /@ Sort@ Join[ FromDigits /@ (Join[{#}, id] & /@ d), FromDigits /@ (Join[id, {#}] & /@ d)]] == {False}];
%t A181333 Select [ Range@ 100, fQ] ; (* _Robert G. Wilson v_, Jan 27 2011 *)
%Y A181333 Cf. A001358.
%K A181333 nonn,easy,base
%O A181333 1,1
%A A181333 _Jonathan Vos Post_, Jan 27 2011