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

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

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: A369276 A038400 A364657 * A225619 A121610 A254752

Adjacent sequences: A254747 A254748 A254749 * A254751 A254752 A254753

Keyword

nonn,base

Author

Stanislav Sykora, Feb 15 2015

Status

approved