A348559 Primes where every other digit is 3 starting with the rightmost digit, and no other digit is 3.

3, 13, 23, 43, 53, 73, 83, 313, 353, 373, 383, 1303, 1373, 2383, 2393, 4363, 4373, 5303, 5323, 5393, 6323, 6343, 6353, 6373, 7393, 8353, 8363, 9323, 9343, 30313, 30323, 31393, 32303, 32323, 32353, 32363, 34303, 34313, 35323, 35353, 35363, 35393, 36313, 36343

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Mathematica

Select[Prime@Range@10000, (n=#; s={EvenQ, OddQ}; t=Take[IntegerDigits@n, {#}]&/@Select[Range@i, #]&/@If[EvenQ[i=IntegerLength@n], s, Reverse@s]; Union@Flatten@First@t=={3}&&FreeQ[Flatten@Last@t, 3])&] (* Giorgos Kalogeropoulos, Oct 22 2021 *)

Prog

(Magma) f3:=func<n|forall{i:i in [1..#Intseq(n) by 2]| Intseq(n)[i] eq 3}>;  fc:=func<n|  forall{i:i in [2..#Intseq(n) by 2]| Intseq(n)[i] ne 3}>; [p:p in PrimesUpTo(40000)|f3(p) and fc(p)]; // Marius A. Burtea, Oct 22 2021
(Python)
from sympy import primerange as primes
def ok(p):
    s = str(p)
    if not all(s[i] == '3' for i in range(-1, -len(s)-1, -2)): return False
    return all(s[i] != '3' for i in range(-2, -len(s)-1, -2))
print(list(filter(ok, primes(1, 36344)))) # Michael S. Branicky, Oct 22 2021
(Python) # faster version for generating large initial segments of sequence
from sympy import isprime
from itertools import product
def eo3(maxdigits): # generator for every other digit is 3, no other 3's
    yield 3
    for d in range(2, maxdigits+1):
        if d%2 == 0:
            for f in "12456789":
                f3 = f + "3"
                for p in product("012456789", repeat=(d-1)//2):
                    yield int(f3 + "".join(p[i]+"3" for i in range(len(p))))
        else:
            for p in product("012456789", repeat=(d-1)//2):
                yield int("3" + "".join(p[i]+"3" for i in range(len(p))))
print(list(filter(isprime, eo3(5)))) # Michael S. Branicky, Oct 22 2021

Crossrefs

Cf. A000040, A348558, A348560, A348561.

Sequence in context: A147473 A030431 A090146 * A133313 A230026 A260798

Adjacent sequences: A348556 A348557 A348558 * A348560 A348561 A348562

Keyword

nonn,base

Author

Lars Blomberg, Oct 22 2021

Status

approved