A348561 Primes where every other digit is 9 starting with the rightmost digit, and no other digit is 9.

19, 29, 59, 79, 89, 919, 929, 1949, 1979, 2909, 2939, 2969, 3919, 3929, 3989, 4909, 4919, 4969, 5939, 6949, 6959, 7919, 7949, 8929, 8969, 90989, 91909, 91939, 91969, 92959, 93949, 93979, 94949, 95929, 95959, 95989, 96959, 96979, 96989, 97919, 98909, 98929

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=={9}&&FreeQ[Flatten@Last@t, 9])&] (* Giorgos Kalogeropoulos, Oct 22 2021 *)
id[n_]:=IntegerDigits[n]; il[n_]:=IntegerLength[n]; eQ[n_]:=EvenQ[il[n]]&&AllTrue[Flatten[Position[id[n], 9]], EvenQ]&&Length[Cases[id[n], 9]]==il[n]/2; oQ[n_]:=OddQ[il[n]]&&
AllTrue[Flatten[Position[id[n], 9]], OddQ]&&Length[Cases[id[n], 9]]==(il[n]+1)/2;
Select[Prime[Range[10^5]], oQ[#]||eQ[#]&] (* Ivan N. Ianakiev, Oct 24 2021 *)

Prog

(Magma) f9:=func<n|forall{i:i in [1..#Intseq(n) by 2]| Intseq(n)[i] eq 9}>;  fc:=func<n|  forall{i:i in [2..#Intseq(n) by 2]| Intseq(n)[i] ne 9}>; [p:p in PrimesUpTo(100000)|f9(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] == '9' for i in range(-1, -len(s)-1, -2)): return False
    return all(s[i] != '9' for i in range(-2, -len(s)-1, -2))
print(list(filter(ok, primes(1, 98930)))) # 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 eo9(maxdigits): # generator for every other digit is 7, no other 7's
    yield 9
    for d in range(2, maxdigits+1):
        if d%2 == 0:
            for f in "12345678":
                f9 = f + "9"
                for p in product("012345678", repeat=(d-1)//2):
                    yield int(f9 + "".join(p[i]+"9" for i in range(len(p))))
        else:
            for p in product("012345678", repeat=(d-1)//2):
                yield int("9" + "".join(p[i]+"9" for i in range(len(p))))
print(list(filter(isprime, eo9(5)))) # Michael S. Branicky, Oct 22 2021

Crossrefs

Cf. A000040, A348558, A348559, A348560.

Sequence in context: A242550 A141311 A090148 * A287313 A136071 A088998

Adjacent sequences: A348558 A348559 A348560 * A348562 A348563 A348564

Keyword

nonn,base

Author

Lars Blomberg, Oct 22 2021

Status

approved