

A260852


Primes in A260851: numbers whose base n expansion is equal to the concatenation of the base n expansions of (1, 2, 3, ..., n1, n, n1, ..., 3, 2, 1).


11




OFFSET

1,1


COMMENTS

Primes of the form (1+r(b)*b)*(r(b)b+1)1 with r(b)=(b^b1)/(b1).
Sequences A173427, A260853  A260859, A173426, A260861  A260866, A260860 list the numbers whose base b expansion is the concatenation of the base b expansions of (1, 2, ..., n, n1, ..., 1). For n < b these are the squares of the repdigits of length n in base b, so the first candidate is the bth term. These are the numbers listed in A260851. For the bases listed in A260343, this candidate is indeed prime: these are the primes listed here.
a(8) = A260851(40) has already 127 digits and is therefore too large to be displayed here.


LINKS

Table of n, a(n) for n=1..7.
D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015


FORMULA

a(n) = A260851(A260343(n)).


PROG

(PARI) for(b=2, 999, ispseudoprime(p=(1+b*c=(b^b1)\(b1))*(cb+1)1)&&print1(p", "))


CROSSREFS

Cf. A173427, A260853  A260859, A173426, A260861  A260866, A260860, A260851.
Sequence in context: A114759 A260871 A260851 * A012832 A102075 A218586
Adjacent sequences: A260849 A260850 A260851 * A260853 A260854 A260855


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Aug 02 2015


STATUS

approved



