A192192 - OEIS

%I #18 Oct 19 2019 10:47:55

%S 9,21,25,57,85,93,121,126,145,161,185,201,206,209,221,237,242,253,265,

%T 289,305,315,326,333,341,365,369,377,381,413,417,437,453,458,490,495,

%U 497,517,537,542,545,565,566,575,578,597,605,633,637,638,649,666,685

%N Numbers whose second arithmetic derivative (A068346) is prime; Polynomial-like numbers of degree 3.

%C The fourth A003415-iteration of a(n) is the first to be 0.

%H Antti Karttunen, <a href="/A192192/b192192.txt">Table of n, a(n) for n = 1..10001</a> (the first 1000 terms from T. D. Noe)

%F For all n, A327969(a(n)) <= 4. - _Antti Karttunen_, Oct 19 2019

%t 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 *)

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o isA192192(n) = isprime(A003415(A003415(n))); \\ _Antti Karttunen_, Oct 19 2019

%Y Cf. A003415, A038554, A068346, A192082, A192189, A192190, A327969, A328240.

%Y Cf. A157037, A328239 (the first and third derivative is prime).

%Y Subsequence of following sequences: A328234, A328244, A328246.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Jun 25 2011

%E More terms from _Olivier Gérard_, Jul 04 2011

%E New primary definition added to the name by _Antti Karttunen_, Oct 19 2019