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A320878 Primes such that iteration of A062028 (n + its digit sum) yields 6 primes in a row.

%I A320878 #20 Feb 10 2019 05:18:59
%S A320878 286330897,286330943,388098901,955201943,1776186851,1854778853,
%T A320878 2559495863,2647782901,3517793911,3628857863,3866728909,3974453911,
%U A320878 4167637819,4269837799,5083007887,5362197829,5642510933,6034811933,8180784851,8214319903
%N A320878 Primes such that iteration of A062028 (n + its digit sum) yields 6 primes in a row.
%C A320878 In contrast to A048523, ..., A048527, this definition uses "at least" for the number of successive primes. This allows easier computation of subsequences of terms which yield even more primes in a row.
%C A320878 One can nonetheless compute the terms of this sequence by considering possible pre-images under A062028 of terms of A048527. This gives the terms which yield exactly 6 primes in a row (i.e., A320878 \ A320879), and one has to take the union with further iterates of this procedure (which successively yields A320879 \ A320880, etc).
%H A320878 Lars Blomberg, <a href="/A320878/b320878.txt">Table of n, a(n) for n = 1..7626</a> (Terms < 10^14. The first 200 from M. F. Hasler)
%H A320878 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_163.htm">Puzzle 163. P+SOD(P)</a>
%F A320878 Numbers n in A048519 for which A062028(n) is in A048527, form the subset A320878 \ A320879.
%o A320878 (PARI) is_A320878(n,p=n)={for(i=1,6, isprime(p=A062028(p))||return);isprime(n)}
%o A320878 forprime(p=286e6,,is_A320878(p)&& print1(p","))
%o A320878 /* much faster, using the precomputed array A048527, as follows: */
%o A320878 PP(n)=select(p->p+sumdigits(p)==n,primes([n-9*#digits(n),n-2])) \\ Returns list of prime predecessors for A062028. (PP(n) nonempty <=> n in A320881.)
%o A320878 A320878=[]; my(S=A048527); while(#S=Set(concat(apply(PP,S))), A320878=setunion(A320878,S)) \\ Yields 211 terms from A048527[1..3000]
%Y A320878 Cf. A062028 (n + digit sum of n), A047791 (A062028(n) is prime), A048519 (primes among these).
%Y A320878 Cf. A048523 .. A048527, A320879.
%Y A320878 a(1) = A090009(7) = start of first chain of 7 primes under iteration of A062028.
%Y A320878 Cf. A320881, A048520.
%Y A320878 Cf. A230093 (number of m s.th. m + (sum of digits of m) = n) and references there.
%K A320878 nonn,base
%O A320878 1,1
%A A320878 _Zak Seidov_ and _M. F. Hasler_, Nov 08 2018