OFFSET
1,3
COMMENTS
Let na and nb represent the indices of the preceding and next A003226(n)'s beginning with a 9, and where (na - nb) >= 3 (note that the first such 'zone' begins with an exception for which the index A003226(na) = 1). Then for na < n < nb and such that n == (na + 1) mod 2, it appears that A003226(n) - a(n) = A003226(n+1) - a(n+1) = k.
In such cases, it also appears that a(n)*a(n+1) = k^2 - k.
EXAMPLE
PROG
(PARI) auto(n) = {n<3 & return(n-1); my(i=10, j=10, b=5, c=6, a=b); for( k=4, n, while(b<=a, b=b^2%i*=10); while(c<=a, c=(2-c)*c%j*=10); a=min(b, c)); a; } \\ A003226
a(n) = {my(m = auto(n), dm = digits(m), dm2 = digits(m^2)); fromdigits(vector(#dm2 - #dm, k, dm2[k])); } \\ Michel Marcus, May 18 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Christopher Hohl, Mar 24 2019
STATUS
approved