A254752 Composite 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, 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

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 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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A202260, A254750, A254751, 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);}
isCompositeSlicingIntoComposites(n,b=10) = isComposite(n) && slicesIntoComposites(n,b);