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%I #12 Dec 11 2015 21:57:29
%S 44,46,48,49,64,66,68,69,84,86,88,94,96,98,99,404,406,408,424,426,428,
%T 444,446,448,454,456,458,464,466,468,469,484,486,488,494,496,498,604,
%U 606,608,609,624,626,628,634,636,638,639,644,646,648,649,654,656,658,664,666,668,669,684,686,688,694,696,698,699,804,806,808,814,816,818,824,826,828
%N Composite numbers such that, in base 10, all their proper prefixes and suffixes represent composites.
%C A proper prefix (or suffix) of a number m is one which is neither void, nor identical to m.
%C Alternative definition: Slicing the decimal expansion of the composite number a(n) in any way into two nonempty parts, each part represents a composite number.
%C This list is infinite because any string of two or more digits selected from {4,6,8} is a member.
%C It is a subsequence of A254750 and shares with it these properties: Each member of a(n) must start, as well as end, with one of the digits {4,6,8,9}. Every proper prefix of each member a(n) is a member of A202260, and every proper suffix is a member of A254755.
%H Stanislav Sykora, <a href="/A254752/b254752.txt">Table of n, a(n) for n = 1..10000</a>
%e 6 is not a member because its expansion cannot be sliced in two.
%e The composite 469 is a member because it is a composite and the slices (4, 69, 46, and 9) are all composites.
%o (PARI) isComposite(n) = (n>2)&&(!isprime(n));
%o slicesIntoComposites(n,b=10) = {my(k=b);if(n<b,return(0););while(n\k>0,if(!isComposite(n\k)||!isComposite(n%k),return(0););k*=b);return(1);}
%o isCompositeSlicingIntoComposites(n,b=10) = isComposite(n) && slicesIntoComposites(n,b);
%Y Cf. A202260, A254750, A254751, A254753, A254754, A254755.
%K nonn,base
%O 1,1
%A _Stanislav Sykora_, Feb 15 2015
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