A348558 Primes where every other digit is 1 starting with the rightmost digit, and no other digit is 1.

31, 41, 61, 71, 101, 131, 151, 181, 191, 2131, 2141, 2161, 3121, 3181, 3191, 5101, 5171, 6101, 6121, 6131, 6151, 7121, 7151, 8101, 8161, 8171, 8191, 9151, 9161, 9181, 10141, 10151, 10181, 12101, 12161, 13121, 13151, 13171, 15101, 15121, 15131, 15161, 16141

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=={1}&&FreeQ[Flatten@Last@t, 1])&] (* Giorgos Kalogeropoulos, Oct 22 2021 *)
eod1Q[p_]:=Module[{r=Reverse[IntegerDigits[p]]}, Union[Take[r, {1, -1, 2}]]=={1}&&FreeQ[ Take[ r, {2, -1, 2}], 1]]; Select[Prime[Range[2000]], eod1Q] (* Harvey P. Dale, May 28 2023 *)

Prog

(Python)
from sympy import primerange as primes
def ok(p):
    s = str(p)
    if not all(s[i] == '1' for i in range(-1, -len(s)-1, -2)): return False
    return all(s[i] != '1' for i in range(-2, -len(s)-1, -2))
print(list(filter(ok, primes(1, 16142)))) # 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 eo1(maxdigits): # generator for every other digit is 1, no other 1's
    yield 1
    for d in range(2, maxdigits+1):
        if d%2 == 0:
            for f in "23456789":
                f1 = f + "1"
                for p in product("023456789", repeat=(d-1)//2):
                    yield int(f1 + "".join(p[i]+"1" for i in range(len(p))))
        else:
            for p in product("023456789", repeat=(d-1)//2):
                yield int("1" + "".join(p[i]+"1" for i in range(len(p))))
print(list(filter(isprime, eo1(5)))) # Michael S. Branicky, Oct 22 2021
(Magma) f1:=func<n|forall{i:i in [1..#Intseq(n) by 2]| Intseq(n)[i] eq 1}>;  fc:=func<n|forall{i:i in [2..#Intseq(n) by 2]| Intseq(n)[i] ne 1}>; [p:p in PrimesUpTo(17000)|f1(p) and fc(p)]; // Marius A. Burtea, Oct 22 2021

Crossrefs

Cf. A000040, A348559, A348560, A348561.

Sequence in context: A099181 A040989 A040969 * A088555 A040178 A089719

Adjacent sequences: A348555 A348556 A348557 * A348559 A348560 A348561

Keyword

nonn,base

Author

Lars Blomberg, Oct 22 2021

Status

approved