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%I #12 Jan 03 2024 10:01:57
%S 324,648,756,4448,4961,4983,5849,11124,34453,37609,54575,97888,860858,
%T 1089693,3143632,3192897,3588047,3768167,5557853,25485909,32899939,
%U 35699309,58260393,64564422,120054389,121554165,356346023,357507563,755438130,990227314
%N 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).
%e If n = 54575, starting from the least significant digit, let us cut the number into the set 5, 75, 575, 4575. We have:
%e sigma(5) = 6;
%e sigma(75) = 124;
%e sigma(575) = 744;
%e sigma(4575) = 7688.
%e Then, starting from the most significant digit, let us cut the number into the set 5, 54, 545, 5457. We have:
%e sigma(5) = 6;
%e sigma(54) = 120;
%e sigma(545) = 660;
%e sigma(5457) = 7776.
%e Finally, 6 + 124 + 744 + 7688 = 6 + 120 + 660 + 7776 = 8562.
%p with(numtheory); P:=proc(q) local a, b, k, n;for n from 2 to q do
%p a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+sigma(trunc(n/10^k)); k:=k+1; od;
%p b:=0; k:=1; while (n mod 10^k)<n do b:=b+sigma(n mod 10^k); k:=k+1; od;
%p if a=b then a:=0; b:=n; while b>0 do a:=10*a+(b mod 10); b:=trunc(b/10); od;
%p if a<>n then print(n); fi; fi; od; end: P(10^9);
%p # alternative
%p for n from 1 do
%p if not isA002113(n) then
%p dgs := convert(n,base,10) ;
%p ndgs := nops(dgs) ;
%p slo := 0 ;
%p shi := 0 ;
%p for sd from 1 to ndgs-1 do
%p lo := add( op(i,dgs)*10^(i-1),i=1..sd) ;
%p slo := slo + numtheory[sigma](lo) ;
%p hi := add( op(-i,dgs)*10^(sd-i),i=1..sd) ;
%p shi := shi + numtheory[sigma](hi) ;
%p end do:
%p if slo = shi then
%p print(n) ;
%p end if;
%p end if;
%p end do: # _R. J. Mathar_, Sep 09 2015
%Y Cf. A000203, A240894-A240903, A241207, A241503.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Apr 24 2014
%E a(16)-a(30) from _Giovanni Resta_, May 23 2016
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