A320882 Primes p such that repeated application of A062028 (add sum of digits) yields two other primes in a row: p, A062028(p) and A062028(A062028(p)) are all prime.

11, 59, 101, 149, 167, 257, 277, 293, 367, 419, 479, 547, 617, 727, 839, 1409, 1559, 1579, 1847, 2039, 2129, 2617, 2657, 2837, 3449, 3517, 3539, 3607, 3719, 4217, 4637, 4877, 5689, 5779, 5807, 5861, 6037, 6257, 6761, 7027, 7489, 7517, 8039, 8741, 8969, 9371, 9377, 10667, 10847, 10937, 11257, 11279, 11299, 11657

Offset: 1

Author

M. F. Hasler, Nov 06 2018

Keywords

• nonn
• base

Comments

"Iterates" the idea of A048519 (p and A062028(p) are prime), also considered in A048523, A048524, A048525, A048526, A048527. (This is the union of A048524, A048525, A048526, A048527 etc. A048525(1) = 277 = a(7).)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A048519: p and A062028(p) are prime.

Cf. A047791, A048520, A006378, A107740, A243441 (p and p + Hammingweight(p) are prime), A243442 (analog for p - Hammingweight(p)).

Cf. A048523, ..., A048527, A320878, A320879, A320880: primes starting a chain of length 2, ..., 9 under iterations of A062028(n) = n + digit sum of n.

Programs

Maple

f:= n -> n + convert(convert(n,base,10),`+`):
filter:= proc(n) local x;
if not isprime(n) then return false fi;
x:= f(n);
isprime(x) and isprime(f(x))
end proc:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Dec 17 2020

PARI

is_A320882(n,p=n)=isprime(p=A062028(p))&&isprime(A062028(p))&&isprime(n) \\ Putting isprime(n) to the end is more efficient for the frequent case when the terms are already known to be prime.
forprime(p=1,14999,isprime(q=A062028(p))&&isprime(A062028(q))&&print1(p","))