More terms from _David Wasserman (wasserma(AT)spawar.navy.mil), _, Aug 25 2005

Numbers n which are divisors of the number formed by concatenating (n-3), (n-2), and (n-1) in that order.

Apart from 11, each other term in this sequence appears to also be a factor of the number formed by concatenating (n+3), (n+2), and (n+1) in that order. All terms appear to be prime. When evaluating concat((n+3),(n+2),(n+1)) - concat((n-3),(n-2),(n-1)) for members larger than 11 the difference appears to always be a number of the form 6(0)...4(0)...2 with the same number of zeros on both sides of the 4. The member will be a prime factor of this number. By factoring numbers of the form 6(0)...4(0)...2 and testing the results, three further members of this sequence have been found: 2723957777, 1260049494294190236301929754269107568067, and 103945392111236434211250670719387720140245499. I have not included these in the list of members above as they were not arrived at through brute force as the first 4 terms were, and there may be other intervening terms.

base,nonn,new

3, 11, 9491, 12258083, 36774249, 2159487563, 2561252691, 2723957777, 6478462689, 8171873331, 333351714587, 146217070005379, 438651210016137, 13919982618156833, 41759947854470499, 1278907806311980217974478364841

base,more,nonn,new

More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Aug 25 2005

Numbers n which are divisors of the number formed by concatenating (n-3), (n-2), and (n-1) in that order.

3, 11, 9491, 12258083

1,1

Apart from 11, each other term in this sequence appears to also be a factor of the number formed by concatenating (n+3), (n+2), and (n+1) in that order. All terms appear to be prime. When evaluating concat((n+3),(n+2),(n+1)) - concat((n-3),(n-2),(n-1)) for members larger than 11 the difference appears to always be a number of the form 6(0)...4(0)...2 with the same number of zeros on both sides of the 4. The member will be a prime factor of this number. By factoring numbers of the form 6(0)...4(0)...2 and testing the results, three further members of this sequence have been found: 2723957777, 1260049494294190236301929754269107568067, and 103945392111236434211250670719387720140245499. I have not included these in the list of members above as they were not arrived at through brute force as the first 4 terms were, and there may be other intervening terms.

a(3)=9491 because 9491 is a factor of 948894899490.

Cf. A069860, A088797, A088798.

base,more,nonn

Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 19 2003

approved