3,1

These numbers are rare. For the case of the reverse concatenation of the consecutive numbers 1,2,3,... I have only found 828180...54321. Certainly, we can reduce the trials by noting that 2/3 of the numbers formed this way are multiples of 3 for the consecutive numbers and 1/3 of the odd consecutive numbers is a multiple of 3 but I do not think that will help much using PARI.

The number corresponding to 54335431...7531 has 10313 digits. The next term, if it exists is greater than 13000. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Feb 21 2009]

31 is the reverse concatenation of the consecutive odd numbers 1 and 3. 31 is

prime. 817815813...531 is the reverse concatenation of the odd numbers 1 to 817.

817815813...531 is a probable prime.

(PARI) revprime2(n) = { y=1; forstep(x=3, n, 2, y=concat(Str(x), Str(y)); z=eval(y); if(ispseudoprime(z), print(x", "z)) ) }

Cf. original concatenation in A038395. [From Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Feb 21 2009]

Sequence in context: A006270 A139888 A079594 this_sequence A041279 A054699 A102267

Adjacent sequences: A089919 A089920 A089921 this_sequence A089923 A089924 A089925

nonn,base

Cino Hilliard (hillcino368(AT)gmail.com), Jan 11 2004

Edited by T. D. Noe (noe(AT)sspectra.com), Oct 30 2008

Added a new term 5433. This number is a probable prime with 20 iterations of Miller-Rabin test. Dmitry Kamenetsky (dkamen(AT)rsise.anu.edu.au), Feb 21 2009