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).

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

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 A351478

Adjacent sequences: A241500 A241501 A241502 * A241504 A241505 A241506

Keyword

nonn,base

Author

Paolo P. Lava, Apr 24 2014

Status

approved