cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A189803 Composite numbers n such that n'' = n'-1 where n' and n'' are the first and the second arithmetic derivative of n.

This page as a plain text file.
%I A189803 #17 Mar 13 2023 13:30:30
%S A189803 9,185,341,377,437,9005,30413,33953,41009,51533,82673,92909,103073,
%T A189803 126509,143009,165773,181793,184973,191309,228653,231713,246893,
%U A189803 291233,311309,316973,319793,329357,353009,358433,374513,398093,405809,431009,460193,467309
%N A189803 Composite numbers n such that n'' = n'-1 where n' and n'' are the first and the second arithmetic derivative of n.
%C A189803 The sequence A189710 (n"=n'-1) includes all prime numbers because p'=1 and p" = 0. Composite numbers are not very frequent.
%C A189803 Are all terms semiprimes? These terms appear to be p*q such that p+q is a term in A054377, which has solutions to the equation n' = n-1. - _T. D. Noe_, Apr 27 2011
%e A189803 9' = 6, 9''= 6'= 5, 9" = 9'- 1 -> 9 is in the sequence.
%o A189803 (PARI) ader(n) = my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1])); \\ A003415
%o A189803 isok(k) = if (!isprime(k), my(d=ader(k)); ader(d) == d - 1); \\ _Michel Marcus_, Mar 13 2023
%Y A189803 Cf. A002808, A003415, A054377, A068346, A189710.
%K A189803 nonn
%O A189803 1,1
%A A189803 _Giorgio Balzarotti_, Apr 27 2011