OFFSET
1,2
COMMENTS
Demlo numbers have been invented and defined by D. R. Kaprekar as numbers of the form L.M.R (concatenated) where L + R = m*A002275(p) and M = m*A002275(k), with 1 <= m <= 9, k = length(M) >= 0, p = length(R) >= length(L) >= p-1, A002275(k) = (10^k-1)/9; zero k or p means that M resp. L and R is/are absent, not zero. In the paper it is shown that any such number can be written as (9L + m)*A002275(k+p).
LINKS
K. R. Gunjikar and D. R. Kaprekar, Theory of Demlo numbers, J. Univ. Bombay, Vol. VIII, Part 3, Nov. 1939, pp. 3-9. [Annotated scanned copy]
EXAMPLE
Any repdigit number (cf. A010785) > 1, any one or two digit number L.R with digit sum m = L + R < 10, and any such number multiplied by a repunit 1...1, L.R*1...1 = L.M.R (where M = digit m repeated length(1...1)-1 times), satisfy the definition.
In Kaprekar's paper it is shown that all Demlo numbers (as defined in the comment) are of that form, cf. formula in comments.
PROG
(PARI) is_A295020(n, d=digits(n), N=#d)={for(r=!n, N, my(p=(1+N-r)\2); r>1 && #Set(d[N-p-r+1..N-p])>1 && return; (!p||((n%10^p>=10^(p-1)||p==1)&&(p==#p=digits(n\10^(p+r)+n%10^p))&&if(r, Set(p)==[d[N-#p]], #Set(p)==1))) && return(1))}
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Nov 17 2017
STATUS
approved