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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A023317 A056436 A334930 * A276694 A380132 A086549

Adjacent sequences: A089821 A089822 A089823 * A089825 A089826 A089827

Keyword

base,nonn

Author

Joseph L. Pe, Jan 09 2004

Status

approved