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

%I A261172 #9 Jun 29 2019 11:23:11
%S A261172 2,3,2,4,3,6,9,10,11,16,12,14,22,18,25,20,2,6,18,14,7,40,31,25,23,20,
%T A261172 22,62,65,68,29,23,38,26,104,6,34,52
%N A261172 Value of b for which A260871(n) = A[b](k), with k = A261171(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 A261172 For more data, see the 2nd column of D. Broadhurst's list of [n, b, k, length(A260871(n))] given in A260871.
%F A261172 A260871(n) = A[a(n)](A261171(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 A261172 A260871(1) = A[2](2), therefore a(1) = 2.
%e A261172 A260871(2) = A[3](3), therefore a(2) = 3.
%e A261172 A260871(3) = A[2](4), therefore a(3) = 2.
%o A261172 (PARI) A261172_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 A261172 Cf. A173427, A260853 - A260859, A173426, A260861 - A260866 and A260860 for A[b] with b=2, ..., b=16 and b=60.
%Y A261172 See also A260852 = { primes of the form A260851(b) = A[b](b), b in A260343 }.
%K A261172 nonn,base
%O A261172 1,1
%A A261172 _M. F. Hasler_, Aug 23 2015