OFFSET
1,1
COMMENTS
Except for a(1) = 111, which is unique, all terms appear infinitely many times and belong to this set of fifteen integers: {21, 23, 27, 29, 33, 39, 57, 59, 69, 71, 83, 87, 99, 101, 107}; see A329914.
The corresponding indices where these integers appear the first time are respectively: 5, 4, 9, 12, 15, 19, 33, 29, 43, 45, 6, 3, 32, 2, 70.
REFERENCES
David Wells, 112359550561797732809 entry, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1997, p. 196.
EXAMPLE
PROG
(PARI) A116436(k) = {local(l, d, lb, ub); d=divisors(10^(k+1)+1); l=[]; lb=10^(k-1); ub=10*lb; for(i=1, #d, if(d[i]>=lb&&d[i]<ub, l=concat(l, [d[i]]))); l}; \\ from A116436
a(n) = {my(v6=[], i=1); while (#v6 < n, v6 = concat(v6, A116436(i)); i++); my(x= v6[n]); my(k=1); while (eval(Str(1, x, 1)) % x, k++); eval(Str(1, x, 1))/x; } \\ Michel Marcus, Feb 10 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Feb 07 2022
STATUS
approved