A241859 1st Arithmetic derivative of numbers with prime arithmetic derivative (A157037).

5, 7, 13, 31, 19, 41, 31, 61, 59, 71, 43, 71, 101, 61, 101, 73, 113, 103, 151, 131, 103, 109, 191, 131, 167, 211, 151, 151, 139, 241, 167, 191, 151, 227, 271, 199, 191, 181, 311, 269, 193, 167, 433, 199, 211, 269, 311, 293, 281, 229, 191, 263, 401, 241, 251

Offset

1,1

Comments

The arithmetic derivative of numbers with prime arithmetic derivative (A157037) leads to a sequence of a selection of prime numbers. It is possible for several numbers to produce the same primes (see A189441). The next arithmetic derivative is A000012, the simplest sequence of positive numbers: the all 1's sequence, A000012=(A157037)’’.

For the arithmetic derivative of n see A003415. - Wolfdieter Lang, May 10 2014

Links

Freimut Marschner, Table of n, a(n) for n = 1..1000

Formula

a(n) = (A157037(n))’.

a(n) = A003415(A157037(n)).

Example

a(10) = (A157037(10))'= (78)' =  (2*3*13)' = 2*3+3*13+2*13 = 71,
a(12) = (A157037(12))'= (105)' = (3*5*7)' = 3*5+5*7+3*7 = 71.

Crossrefs

Cf. A157037, A003415, A189441.

Sequence in context: A230115 A182342 A178648 * A293059 A179625 A141191

Adjacent sequences: A241856 A241857 A241858 * A241860 A241861 A241862

Keyword

nonn

Author

Freimut Marschner, Apr 30 2014

Status

approved