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

286330897, 286330943, 388098901, 955201943, 1776186851, 1854778853, 2559495863, 2647782901, 3517793911, 3628857863, 3866728909, 3974453911, 4167637819, 4269837799, 5083007887, 5362197829, 5642510933, 6034811933, 8180784851, 8214319903

Offset: 1

Author

Zak Seidov and M. F. Hasler, Nov 08 2018

Keywords

• nonn
• base

Comments

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.

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).

Links

• Lars Blomberg, Table of n, a(n) for n = 1..7626 (Terms < 10^14. The first 200 from M. F. Hasler)
• Carlos Rivera, Puzzle 163. P+SOD(P)

Crossrefs

Cf. A062028 (n + digit sum of n), A047791 (A062028(n) is prime), A048519 (primes among these).

Cf. A048523 .. A048527, A320879.

a(1) = A090009(7) = start of first chain of 7 primes under iteration of A062028.

Cf. A320881, A048520.

Cf. A230093 (number of m s.th. m + (sum of digits of m) = n) and references there.

Programs

PARI

is_A320878(n,p=n)={for(i=1,6, isprime(p=A062028(p))||return);isprime(n)}
forprime(p=286e6,,is_A320878(p)&& print1(p","))
/* much faster, using the precomputed array A048527, as follows: */
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.)
A320878=[]; my(S=A048527); while(#S=Set(concat(apply(PP,S))), A320878=setunion(A320878,S)) \\ Yields 211 terms from A048527[1..3000]

Formula

Numbers n in A048519 for which A062028(n) is in A048527, form the subset A320878 \ A320879.