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

Author

Stanislav Sykora, Feb 15 2015

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A202260, A254751, A254752, A254753, A254754, A254755.

Programs

PARI

isComposite(n) = (n>2)&&(!isprime(n));
slicesIntoComposites(n,b=10) = {my(k=b);if(n0,if(!isComposite(n\k)||!isComposite(n%k),return(0););k*=b);return(1);}