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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). 5
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 (list; graph; refs; listen; history; text; internal format)
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 A202094

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

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Last modified September 16 12:34 EDT 2019. Contains 327098 sequences. (Running on oeis4.)