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A241503
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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).
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5
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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
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..49.
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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Cf. A000010, A240894-A240903, A241207, A241502.
Sequence in context: A179899 A085926 A071263 * A226186 A325301 A351478
Adjacent sequences: A241500 A241501 A241502 * A241504 A241505 A241506
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KEYWORD
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nonn,base
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AUTHOR
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Paolo P. Lava, Apr 24 2014
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STATUS
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approved
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