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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
12, 21, 34, 36, 43, 46, 58, 63, 64, 79, 85, 97, 338, 356, 374, 376, 426, 456, 544, 580, 593, 698, 845, 886, 947, 963, 2071, 2162, 3188, 4187, 5939, 8806, 8955, 8968, 9409, 9944, 34414, 34940, 38754, 41789, 42844, 44437, 45876, 47730, 49060, 54424, 58774, 67304, 69340 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

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

phi(4) = 2;

phi(54) = 18;

phi(754) = 336;

phi(8754) = 2916.

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

phi(3) = 2;

phi(38) = 18;

phi(387) = 252;

phi(3875) = 3000.

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

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

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

CROSSREFS

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

Sequence in context: A179899 A085926 A071263 * A226186 A325301 A219542

Adjacent sequences:  A241500 A241501 A241502 * A241504 A241505 A241506

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Apr 24 2014

STATUS

approved

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Last modified September 16 10:23 EDT 2019. Contains 327094 sequences. (Running on oeis4.)