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A244077
Consider a 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 n’ = Sum_{i=1..k-1}{Sum_{j=1..i}{d_(k-j+1)*10^(i-j)}}’, where n’ is the arithmetic derivative of n (see example below).
1
23, 29, 31, 37, 53, 59, 71, 73, 79, 113, 131, 137, 139, 173, 179, 191, 193, 197, 199, 6437, 8339, 14473, 60827, 95611, 107813
OFFSET
1,1
COMMENTS
From 23 to 199 only primes, then composites.
EXAMPLE
If n = 14473, starting from the most significant digit, let us cut the number into the set {1, 14, 144, 1447}. We have:
1’ = 0;
14’ = 9;
144’ = 384;
1447’ = 1.
Finally, 0 + 9 + 384 + 1 = 14473’ = 394.
MAPLE
with(numtheory); P:=proc(q) local a, c, k, n, p;
for n from 10 to q do
a:=0; k:=1; while trunc(n/10^k)>0 do c:=trunc(n/10^k);
a:=a+c*add(op(2, p)/op(1, p), p=ifactors(c)[2]); k:=k+1; od;
if a=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]) then print(n);
fi; od; end: P(10^10);
KEYWORD
nonn,more,base
AUTHOR
Paolo P. Lava, Jun 19 2014
STATUS
approved