A089824 Primes p such that the next prime after p can be obtained from p by adding the sum of the digits of p.

11, 13, 101, 103, 181, 293, 631, 701, 811, 1153, 1171, 1409, 1801, 1933, 2017, 2039, 2053, 2143, 2213, 2521, 2633, 3041, 3089, 3221, 3373, 3391, 3469, 3643, 3739, 4057, 4231, 5153, 5281, 5333, 5449, 5623, 5717, 6053, 6121, 6301, 7043, 7333, 8101, 8543, 9241

Offset: 1

Author

Joseph L. Pe, Jan 09 2004

Keywords

• base
• nonn

Comments

I call these primes (additive) "pointer primes", in the sense that such primes p "point" to the next prime after p when the sum of the digits of p is added to p.

Examples

			13 + sum of digits of 13 = 17, which is the next prime after 13. Hence 13 belongs to the sequence.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Programs

Maple

a:= proc(n) option remember; local p, q;
      p:= a(n-1); q:= nextprime(p);
      do p:= q; q:= nextprime(p);
         if add(i, i=convert(p, base, 10))=q-p then break fi
      od; p
    end: a(1):= 11:
seq(a(n), n=1..50);  # Alois P. Heinz, Nov 18 2017

Mathematica

r = {}; Do[p = Prime[i]; q = Prime[i + 1]; If[p + Apply[Plus, IntegerDigits[p]] == q, r = Append[r, p]], {i, 1, 10^6}]; r
Transpose[Select[Partition[Prime[Range[1000]],2,1],#[[2]]==#[[1]]+Total[ IntegerDigits[ #[[1]]]]&]][[1]] (* Harvey P. Dale, Apr 20 2013 *)

Python

from sympy import isprime, nextprime
def ok(n): return isprime(n) and sum(map(int, str(n))) + n == nextprime(n)
print([k for k in range(10**4) if ok(k)]) # Michael S. Branicky, Dec 07 2024