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A192192
Numbers whose second arithmetic derivative (A068346) is prime; Polynomial-like numbers of degree 3.
11
9, 21, 25, 57, 85, 93, 121, 126, 145, 161, 185, 201, 206, 209, 221, 237, 242, 253, 265, 289, 305, 315, 326, 333, 341, 365, 369, 377, 381, 413, 417, 437, 453, 458, 490, 495, 497, 517, 537, 542, 545, 565, 566, 575, 578, 597, 605, 633, 637, 638, 649, 666, 685
OFFSET
1,1
COMMENTS
The fourth A003415-iteration of a(n) is the first to be 0.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10001 (the first 1000 terms from T. D. Noe)
FORMULA
For all n, A327969(a(n)) <= 4. - Antti Karttunen, Oct 19 2019
MATHEMATICA
dn[0] = 0; dn[1] = 0; dn[n_?Negative] := -dn[-n]; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Total[n*f[[2]]/f[[1]]]]]; Select[Range[1000], dn[dn[dn[#]]] == 1&] (* T. D. Noe, Mar 07 2013 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA192192(n) = isprime(A003415(A003415(n))); \\ Antti Karttunen, Oct 19 2019
CROSSREFS
Cf. A157037, A328239 (the first and third derivative is prime).
Subsequence of following sequences: A328234, A328244, A328246.
Sequence in context: A273202 A338909 A173456 * A053795 A100490 A173250
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jun 25 2011
EXTENSIONS
More terms from Olivier Gérard, Jul 04 2011
New primary definition added to the name by Antti Karttunen, Oct 19 2019
STATUS
approved