A083284 Numbers m such that m and m+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.

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

Offset

1,1

Comments

The only consecutive brilliant numbers are {9, 10} and {14, 15}; and for m > 14 there are no brilliant constellations of the form {m, m+(2k+1)} or equivalently {n, 2k+m+1} with k >= 0. Proof: One of m and 2k+m+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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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

Crossrefs

Cf. A078972.

Sequence in context: A003393 A089668 A257922 * A350613 A152218 A152463

Adjacent sequences: A083281 A083282 A083283 * A083285 A083286 A083287

Keyword

base,easy,nonn

Author

Jason Earls, Jun 03 2003

Status

approved