A260852 Primes in A260851: numbers whose base n expansion is equal to the concatenation of the base n expansions of (1, 2, 3, ..., n-1, n, n-1, ..., 3, 2, 1).

13, 439, 27961, 522134761, 21107054541321649, 12345678910987654321, 24197857203266734883076090685781525281

Offset: 1

Author

M. F. Hasler, Aug 02 2015

Keywords

• nonn
• base

Comments

Primes of the form (1+r(b)*b)*(r(b)-b+1)-1 with r(b)=(b^b-1)/(b-1).

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, n-1, ..., 1). For n < b these are the squares of the repdigits of length n in base b, so the first candidate is the b-th 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

• D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Cf. A173427, A260853 - A260859, A173426, A260861 - A260866, A260860, A260851.

Programs

PARI

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

Formula

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