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A241503 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}{phi(Sum_{j=1..i}{d_(j)*10^(j-1)})}} = Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below). 5

%I

%S 12,21,34,36,43,46,58,63,64,79,85,97,338,356,374,376,426,456,544,580,

%T 593,698,845,886,947,963,2071,2162,3188,4187,5939,8806,8955,8968,9409,

%U 9944,34414,34940,38754,41789,42844,44437,45876,47730,49060,54424,58774,67304,69340

%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}{phi(Sum_{j=1..i}{d_(j)*10^(j-1)})}} = Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below).

%e If n = 38754, starting from the least significant digit, let us cut the number into the set 4, 54, 754, 8754. We have:

%e phi(4) = 2;

%e phi(54) = 18;

%e phi(754) = 336;

%e phi(8754) = 2916.

%e Then, starting from the most significant digit, let us cut the number into the set 3, 38, 387, 3875. We have:

%e phi(3) = 2;

%e phi(38) = 18;

%e phi(387) = 252;

%e phi(3875) = 3000.

%e Finally, 2 + 18 + 336 + 2916 = 2 + 18 + 252 + 3000 = 3272.

%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+phi(trunc(n/10^k)); k:=k+1; od;

%p b:=0; k:=1; while (n mod 10^k)<n do b:=b+phi(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);

%Y Cf. A000010, A240894-A240903, A241207, A241502.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Apr 24 2014

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Last modified October 23 05:56 EDT 2019. Contains 328335 sequences. (Running on oeis4.)