

A254752


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


6



44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 94, 96, 98, 99, 404, 406, 408, 424, 426, 428, 444, 446, 448, 454, 456, 458, 464, 466, 468, 469, 484, 486, 488, 494, 496, 498, 604, 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
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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 the composite number a(n) in any way into two nonempty parts, each part represents a composite number.
This list is infinite because any string of two or more digits selected from {4,6,8} is a member.
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.


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.
The composite 469 is a member because it is a composite and the slices (4, 69, 46, and 9) 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); }
isCompositeSlicingIntoComposites(n, b=10) = isComposite(n) && slicesIntoComposites(n, b);


CROSSREFS

Cf. A202260, A254750, A254751, A254753, A254754, A254755.
Sequence in context: A254750 A225619 A121610 * A063837 A178755 A182261
Adjacent sequences: A254749 A254750 A254751 * A254753 A254754 A254755


KEYWORD

nonn,base


AUTHOR

Stanislav Sykora, Feb 15 2015


STATUS

approved



