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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 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)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

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)