cp's OEIS Frontend

A254750 Numbers such that, in base 10, all their proper prefixes and suffixes represent composites.

%I A254750 #13 Dec 11 2015 21:58:28
%S A254750 44,46,48,49,64,66,68,69,84,86,88,89,94,96,98,99,404,406,408,409,424,
%T A254750 426,428,444,446,448,449,454,456,458,464,466,468,469,484,486,488,494,
%U A254750 496,498,499,604,606,608,609,624,626,628,634,636,638
%N A254750 Numbers such that, in base 10, all their proper prefixes and suffixes represent composites.
%C A254750 A proper prefix (or suffix) of a number m is one which is neither void, nor identical to m.
%C A254750 Alternative definition: Slicing the decimal expansion of a(n) in any way into two nonempty parts, each part represents a composite number.
%C A254750 The list is infinite because any string of two or more digits selected from {4,6,8} represents a member.
%C A254750 Each member a(n) starts, as well as ends, with one of the digits {4,6,8,9}.
%C A254750 Every proper prefix of each member a(n) is a member of A202260, and every proper suffix is a member of A254755.
%C A254750 The sequence is a union of A254752 and A254754.
%H A254750 Stanislav Sykora, <a href="/A254750/b254750.txt">Table of n, a(n) for n = 1..10000</a>
%e A254750 6 is not a member because its expansion cannot be sliced in two.
%e A254750 638 is a member because (6, 38, 63, and 8) are all composites.
%o A254750 (PARI) isComposite(n) = (n>2)&&(!isprime(n));
%o A254750 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);}
%Y A254750 Cf. A202260, A254751, A254752, A254753, A254754, A254755.
%K A254750 nonn,base
%O A254750 1,1
%A A254750 _Stanislav Sykora_, Feb 15 2015