

A254750


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


7



44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 89, 94, 96, 98, 99, 404, 406, 408, 409, 424, 426, 428, 444, 446, 448, 449, 454, 456, 458, 464, 466, 468, 469, 484, 486, 488, 494, 496, 498, 499, 604, 606, 608, 609, 624, 626, 628, 634, 636, 638
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

A proper prefix (or suffix) of a number m is one which is neither void, nor identical to m.
Alternative definition: Slicing the decimal expansion of a(n) in any way into two nonempty parts, each part represents a composite number.
The list is infinite because any string of two or more digits selected from {4,6,8} represents a member.
Each member a(n) starts, as well as ends, 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.
The sequence is a union of A254752 and A254754.


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..10000


EXAMPLE

6 is not a member because its expansion cannot be sliced in two.
638 is a member because (6, 38, 63, and 8) are all composites.


PROG

(PARI) isComposite(n) = (n>2)&&(!isprime(n));
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); }


CROSSREFS

Cf. A202260, A254751, A254752, A254753, A254754, A254755.
Sequence in context: A112815 A242934 A038400 * A225619 A121610 A254752
Adjacent sequences: A254747 A254748 A254749 * A254751 A254752 A254753


KEYWORD

nonn,base


AUTHOR

Stanislav Sykora, Feb 15 2015


STATUS

approved



