A178540 a(n) is the smallest n-digit non-palindromic number m such that sum of the prime factors of m is equal to sum of the prime factors of reversal(m).

45, 250, 1131, 12441, 109416, 1002921, 10009577, 100022593, 1000081008, 10000401424, 100000835544, 1000001449713, 10000013519782, 100000013605380, 1000000081310530

Offset

2,1

Comments

If 10 doen't divide n, number of digits of n is l and both numbers n & reversal(n) have the same sum of prime factors then for all positive numbers k, n*(10^(k*l)-1)/(10^l-1) has the same property (See the mentioned link).

Links

Table of n, a(n) for n=2..16.

Carlos Rivera SOPF(N)=SOP(RN)

Example

250 = 2*5*5*5, reversal(250) = 2*2*13, sum of the prime factors of both these are equal, namely 17 and since 250 is the smallest 3-digit number with this property, so
  a(3) = 250.

Mathematica

r[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; sop[n_]:=(b=FactorInteger[n]; l=Length[b]; Sum[b[[k]][[1]]*b[[k]][[2]], {k, l}]); a[n_]:=(For[k=1, 10^(n-1)+kŠr[10^(n-1)+k]||sop[10^(n-1)+k]¹sop[r[10^(n-1)+k]], k++]; 10^(n-1)+k)

Crossrefs

Cf. A001414, A004086.

Sequence in context: A172118 A127073 A089549 * A351534 A296326 A064561

Adjacent sequences: A178537 A178538 A178539 * A178541 A178542 A178543

Keyword

nonn,base

Author

J. M. Bergot & Farideh Firoozbakht, Dec 24 2010

Status

approved