A241502 Consider a non-palindromic number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(j)*10^(j-1)})} = Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).

324, 648, 756, 4448, 4961, 4983, 5849, 11124, 34453, 37609, 54575, 97888, 860858, 1089693, 3143632, 3192897, 3588047, 3768167, 5557853, 25485909, 32899939, 35699309, 58260393, 64564422, 120054389, 121554165, 356346023, 357507563, 755438130, 990227314

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Example

If n = 54575, starting from the least significant digit, let us cut the number into the set 5, 75, 575, 4575. We have:
sigma(5) = 6;
sigma(75) = 124;
sigma(575) = 744;
sigma(4575) = 7688.
Then, starting from the most significant digit, let us cut the number into the set 5, 54, 545, 5457. We have:
sigma(5) = 6;
sigma(54) = 120;
sigma(545) = 660;
sigma(5457) = 7776.
Finally, 6 + 124 + 744 + 7688 = 6 + 120 + 660 + 7776 = 8562.

Maple

with(numtheory); P:=proc(q) local a, b, k, n; for n from 2 to q do
a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+sigma(trunc(n/10^k)); k:=k+1; od;
b:=0; k:=1; while (n mod 10^k)<n do b:=b+sigma(n mod 10^k); k:=k+1; od;
if a=b then a:=0; b:=n; while b>0 do a:=10*a+(b mod 10); b:=trunc(b/10); od;
if a<>n then print(n); fi; fi; od; end: P(10^9);
# alternative
for n from 1 do
    if not isA002113(n) then
        dgs := convert(n, base, 10) ;
        ndgs := nops(dgs) ;
        slo := 0 ;
        shi := 0 ;
        for sd from 1 to ndgs-1 do
            lo := add( op(i, dgs)*10^(i-1), i=1..sd) ;
            slo := slo + numtheory[sigma](lo) ;
            hi := add( op(-i, dgs)*10^(sd-i), i=1..sd) ;
            shi := shi + numtheory[sigma](hi) ;
        end do:
        if slo = shi then
            print(n) ;
        end if;
    end if;
end do: # R. J. Mathar, Sep 09 2015

Crossrefs

Cf. A000203, A240894-A240903, A241207, A241503.

Sequence in context: A045287 A096526 A111278 * A014792 A287634 A329613

Adjacent sequences: A241499 A241500 A241501 * A241503 A241504 A241505

Keyword

nonn,base

Author

Paolo P. Lava, Apr 24 2014

Extensions

a(16)-a(30) from Giovanni Resta, May 23 2016

Status

approved