

A083284


Numbers n such that n and n+2 are both brilliant numbers, where brilliant numbers are semiprimes whose prime factors have an equal number of decimal digits, or whose prime factors are equal.


1



4, 527, 779, 869, 899, 1079, 1157, 1271, 1679, 4187, 6497, 6887, 24287, 24881, 25019, 29591, 35237, 37127, 37769, 38807, 39269, 39911, 41309, 43361, 44831, 45347, 46001, 46127, 47261, 48509, 48929, 51809, 52907, 54389, 55481, 55751, 55961
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OFFSET

1,1


COMMENTS

The only consecutive brilliant numbers are {9, 10} and {14, 15}; and for n > 14 there are no brilliant constellations of the form {n, n+(2k+1)} or equivalently {n, 2k+n+1} with k >= 0. Proof: One of n and 2k+n+1 will be even. And there are no even brilliant numbers > 14 since they must have the form 2*p where p is a prime having only one digit.


LINKS

Table of n, a(n) for n=1..37.


EXAMPLE

a(3)= 779 because 779=19*41 and 781=11*71.


CROSSREFS

Cf. A078972.
Sequence in context: A003393 A089668 A257922 * A152218 A152463 A295206
Adjacent sequences: A083281 A083282 A083283 * A083285 A083286 A083287


KEYWORD

base,easy,nonn


AUTHOR

Jason Earls, Jun 03 2003


STATUS

approved



