A392563 a(n) is the least number that can be written in exactly n ways as p + r, where p is a prime and r is an anagram of p.

1, 4, 44, 88, 299, 898, 776, 1106, 5008, 4994, 6325, 5654, 5104, 6776, 8888, 8998, 9494, 8585, 10706, 43444, 11009, 12625, 26666, 44554, 50504, 31211, 53332, 66556, 54443, 54344, 39998, 11110, 28888, 67777, 55556, 32221, 33332, 91108, 55564, 89908, 108088, 106706, 107062, 89888, 71110, 66662

Offset

0,2

Comments

Leading zeros are not allowed.

Links

Robert Israel, Table of n, a(n) for n = 0..559

Formula

A393958(a(n)) = n.

Example

a(5) = 898 because 898 = 179 + 719 = 269 + 629 = 359 + 539 = 449 + 449 = 719 + 179 can be written in exactly 5 ways as the sum of a prime and an anagram of that prime, and 898 is the least number that works.

Maple

g:= proc(n) local d, F, i;
  F:= convert(n, base, 10); d:= nops(F);
  map(t -> n + add(t[i]*10^(i-1), i=1..d), select( t -> t[-1] <> 0, combinat:-permute(F)))
end proc:
N:= 1000000: V:= Vector(N):
for p in select(isprime, [2, seq(i, i=3..N, 2)]) do
  v:= select(`<=`, g(p), N);
  V[v]:= V[v]+~ 1
od:
R:= Array(0..max(V)):
for i from 1 to N do
if R[V[i]] = 0 then R[V[i]]:= i fi
od:
if not member(0, R, 'k0') then k0:= max(V)+1 fi;
convert(R[0..k0-1], list);

Crossrefs

Cf. A393958.

Sequence in context: A284065 A063837 A389757 * A344871 A071125 A193448

Adjacent sequences: A392560 A392561 A392562 * A392564 A392565 A392566

Keyword

nonn,base,look

Author

Robert Israel, Mar 04 2026

Status

approved