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A254754 Prime numbers such that, in base 10, all their proper prefixes and suffixes represent composites. 7
89, 409, 449, 499, 809, 4049, 4549, 4649, 4909, 4969, 6299, 6469, 6869, 6899, 6949, 8009, 8039, 8069, 8209, 8609, 8669, 8699, 8849, 9049, 9209, 9649, 9949, 40009, 40099, 40609, 40639, 40699, 40849, 42209, 42649, 44249, 44699, 45949, 46049, 46099 (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: Slice the decimal expansion of the prime number a(n) in any way into two nonempty parts; then both parts represent a composite number.

This sequence is a subset of A254750. Each member a(n) must start with one of the digits {4,6,8,9} and end with 9.

Every proper prefix of each member a(n) is a member of A202260, and every proper suffix is a member of A254755.

These numbers are rare and tend to become rarer with increasing n, but the sequence does not seem to terminate (for example, 4*10^28 + 9 is a member).

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..20000

EXAMPLE

7 is not a member because its expansion cannot be sliced in two.

The prime 4969 is a member because it is a prime and the slices (4, 969, 49, 69, 496, 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); }

isPrimeSlicingIntoComposites(n, b=10) = isprime(n) && slicesIntoComposites(n, b);

CROSSREFS

Cf. A202260, A254750, A254751, A254752, A254753, A254755.

Sequence in context: A244777 A107192 A061372 * A083473 A142186 A142757

Adjacent sequences:  A254751 A254752 A254753 * A254755 A254756 A254757

KEYWORD

nonn,base

AUTHOR

Stanislav Sykora, Feb 15 2015

STATUS

approved

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Last modified May 26 03:13 EDT 2017. Contains 287073 sequences.