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 A244078 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_(j)*10^(j-1)}}’, where n’ is the arithmetic derivative of n (see example below). 1
 13, 17, 23, 37, 43, 53, 67, 73, 83, 97, 131, 211, 241, 271, 311, 331, 431, 461, 541, 571, 631, 641, 661, 761, 811, 911, 941, 971, 1601, 3701, 5101, 5701, 6101, 6701, 8101, 9601, 13001, 16138, 18497, 19001, 22879, 24001, 54001, 69001, 93001, 97001, 99361, 270001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Mainly primes. LINKS EXAMPLE If n = 16138, starting from the least significant digit, let us cut the number into the set {8, 38, 138, 6138}. We have: 8’ = 12; 38’ = 21; 138’ = 121; 6138’ = 7917. Finally, 12 + 21 + 121 + 7917 = 16138’ = 8071. MAPLE with(numtheory); P:=proc(q) local a, c, k, n, p; for n from 10 to q do a:=0; k:=1; while (n mod 10^k)

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Last modified August 8 16:09 EDT 2022. Contains 356015 sequences. (Running on oeis4.)