A261171 Value of k for which A260871(n) = A[b](k), with b = A261172(n); A[b](k) = the number whose base-b representation is the concatenation of the base-b representations of (1, ..., k, k-1, ..., 1).

2, 3, 4, 4, 5, 6, 9, 10, 13, 16, 16, 21, 23, 23, 29, 28, 38, 39, 33, 34, 41, 40, 37, 37, 41, 42, 44, 64, 77, 82, 75, 83, 83, 87, 104, 104, 86, 94

Offset: 1

Author

M. F. Hasler, Aug 23 2015

Keywords

• nonn
• base

Comments

For more data, see the 3rd column of D. Broadhurst's list of [n, b, k, length(A260871(n))] given in A260871.

This and the companion sequence A261172 are a compact way of recording the very large primes listed in A260871 by means of the k- and b-value such that A260871(n) = A[A261172(n)](A261171(n)). See A261170 for the number of decimal digits of these primes. - M. F. Hasler, Sep 15 2015

Examples

			A260871(1) = A[2](2), therefore a(1) = 2.
A260871(2) = A[3](3), therefore a(2) = 3.
A260871(3) = A[2](4), therefore a(3) = 4.
		

Crossrefs

Cf. A173427, A260853 - A260859, A173426, A260861 - A260866 and A260860 for A[b] with b=2, ..., b=16 and b=60.

See also A260852 = { primes of the form A260851(b) = A[b](b), b in A260343 }.

Programs

PARI

A261171_list(LIM=1e499)={my(A=List(),p,d);for(b=2,9e9,for(n=b,9e9,if(LIMb)));ispseudoprime(p)&&listput(A,[log(p),n])));apply(t->t[2],vecsort(A))}

Formula

A260871(n) = A[A261172(n)](a(n)), where A[b](k) = Sum_{i=1..#d} d[i]*b^(#d-i), d = concatenation of (1, 2, ..., k, k-1, ..., 1) all written in base b.