A261171 - OEIS

%I #12 Jun 29 2019 11:23:08

%S 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,

%T 42,44,64,77,82,75,83,83,87,104,104,86,94

%N 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).

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

%C 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

%F 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.

%e A260871(1) = A[2](2), therefore a(1) = 2.

%e A260871(2) = A[3](3), therefore a(2) = 3.

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

%o (PARI) A261171_list(LIM=1e499)={my(A=List(),p,d);for(b=2,9e9,for(n=b,9e9,if(LIM<p=sum(i=1,#d=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),d[i]*b^(#d-i)),break(2-(n>b)));ispseudoprime(p)&&listput(A,[log(p),n])));apply(t->t[2],vecsort(A))}

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

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

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Aug 23 2015