A394623 - OEIS

A394623

Primes containing as many 0's as 1's, 2's as 3's, 4's as 5's, 6's as 7's, and 8's as 9's.

23, 67, 89, 1607, 2389, 2543, 4051, 4253, 4523, 4567, 4657, 5647, 5849, 6547, 6701, 8293, 8329, 8923, 9283, 100189, 100213, 100981, 101089, 101203, 102013, 102031, 102103, 102233, 102301, 102367, 102673, 102763, 102983, 103289, 105401, 105467, 106273, 108109, 108293, 108769, 108923, 108967

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OFFSET

1,1

COMMENTS

Primes whose decimal representation contains the same number of i's as (i+1)'s for i = 0, 2, 4, 6 and 8.

All terms have an even number of digits.

LINKS

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

EXAMPLE

a(4) = 1607 is a term because 1607 is prime and has the same number (1) of 0's and 1's, the same number (1) of 6's and 7's, and the same number (0) of all other digits.

MAPLE

filter:= proc(n) local L; L:= convert(n, base, 10);

andmap(i -> numboccur(i, L) = numboccur(i+1, L), [0, 2, 4, 6, 8]) and isprime(n)

end proc:

select(filter, [seq(seq(x, x=10^(d-1)+1 .. 10^d-1, 2), d=2..6, 2)]);

MATHEMATICA

pQ[p_]:= AllTrue[{0, 2, 4, 6, 8}, Count[IntegerDigits[p], #]==Count[IntegerDigits[p], #+1]&]; Select[Prime[Range[10363]], pQ] (* James C. McMahon, Mar 30 2026 *)

CROSSREFS

Sequence in context: A241212 A052087 A030458 * A053559 A322414 A031376

Adjacent sequences: A394620 A394621 A394622 * A394624 A394625 A394626

KEYWORD

nonn,base

AUTHOR

Robert Israel, Mar 26 2026

STATUS

approved