A392836 Primes that cannot be written as p + r where p is a prime and r is an anagram of p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 223, 227, 229, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 313, 317, 331, 337

Offset

1,1

Comments

Primes not in A393975.

Leading zeros are not allowed in anagrams.

We expect that most large primes are not terms.

If p and q are the greatest prime < 10^d and least prime > 10^d respectively, any prime between 10^d + p and 10^d + q must be a term. Thus we expect there to be infinitely many terms.

Links

Robert Israel, Table of n, a(n) for n = 1..9428

Example

a(6) = 13 is a term because there is no prime p such that 13 - p is an anagram of p.

Maple

g:= proc(n) local d, L, i;
  L:= convert(n, base, 10); d:= nops(L);
  select(isprime, convert(map(t -> n + add(t[i]*10^(i-1), i=1..d), select( t -> t[-1] <> 0, combinat:-permute(L))), set))
end proc:
P:= select(isprime, {2, seq(i, i=3..10^4, 2)}): S:= P:
for p in P do S:= S minus g(p); od:
sort(convert(S, list));

Crossrefs

Cf. A393975.

Sequence in context: A216887 A095320 A238853 * A077359 A057448 A049551

Adjacent sequences: A392833 A392834 A392835 * A392837 A392838 A392839

Keyword

nonn,base,look

Author

Robert Israel, Mar 15 2026

Status

approved