A020469 -id:A020469 - cp's OEIS frontend

A174844 Primes that generate three other primes when 2, 6, and 8, respectively, are subtracted from each digit of their decimal representations.

9898898899, 889898999999, 889989889889, 898888889989, 989899998889, 999988988989, 988898889999899, 989998888989889, 98888888989989899, 99999998998988999, 888898989989989999, 888998889889898899, 889888889998888999, 889888898999988989, 889988888998998889

Offset: 1

Rick L. Shepherd, Mar 30 2010

Subsequence of A020472. The primes generated from the subtractions are in A020469, A020458, and A020449, respectively. Final digits are necessarily 9 (here), then 7, 3, and 1. Because leading 8's are permitted in the terms here, the primes generated by subtracting 8's may have fewer digits than the others.

			9898898899 is prime and so are 7676676677, 3232232233, and 1010010011, so it is a term. Although 9349, 9349-2222=7127, 9349-6666=2683, and 9349-8888=461 are four primes, 9349 is not a term as subtracting 6 or 8 from the digits 3 and 4 is not possible (no "borrowing" is permitted).

Robert Israel, Table of n, a(n) for n = 1..1188

Cf. A020472, A020469, A020458, A020449.

Res:= NULL: count:= 0:
for d from 2 while count < 100 do
  v:= (10^d-1)/9;
  for m from 1 to d do
    if m mod 3 <> 0 and 2*d+m mod 3 <> 0 then
      for S in combinat:-choose([$1..(d-2)],m-1) do
        q:= 1+add(10^i,i=S);
        if andmap(isprime, [q, 2*v+q, 6*v+q, 8*v+q]) then
           count:= count+1; Res:= Res, 8*v+q;
        fi
      od;
    fi
  od;
od:
sort([Res]); # Robert Israel, Nov 14 2022

okQ[n_]:=Module[{idn=IntegerDigits[n]},And@@PrimeQ[FromDigits/@ {idn-2, idn-6, idn-8}]]; Select[Flatten[Table[Select[FromDigits/@ Tuples[ {8,9},n], PrimeQ],{n,18}]],okQ] (* Harvey P. Dale, Jul 27 2011 *)

{/* Program based on that of M. F. Hasler in A020472. */
for(nd=1, 20, p=vector(nd, i, 10^(nd-i))~; r=(10^nd-1)/9;
forvec(v=vector(nd, i, [8+(i==nd), 9]), q=v*p; isprime(q) &&
isprime(q-2*r ) && isprime(q-6*r ) && isprime(q-8*r ) && print1(q", ")))}

from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    for d in count(2):
        subs = list(map(int, ["2"*d, "6"*d, "8"*d]))
        for first in product("89", repeat=d-1):
            t = int("".join(first) + "9")
            if isprime(t) and all(isprime(t-s) for s in subs): yield t
print(list(islice(agen(), 15))) # Michael S. Branicky, Nov 15 2022

A386354 Primes without {6, 7} as digits.

Original entry on oeis.org

2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 59, 83, 89, 101, 103, 109, 113, 131, 139, 149, 151, 181, 191, 193, 199, 211, 223, 229, 233, 239, 241, 251, 281, 283, 293, 311, 313, 331, 349, 353, 359, 383, 389, 401, 409, 419, 421, 431, 433, 439, 443, 449, 491, 499

Offset: 1

Jason Bard, Jul 20 2025

Intersection of A038614 and A038615.

Cf. A000040, A020469, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 1, 2, 3, 4, 5, 8, 9]];

Select[Prime[Range[120]], DigitCount[#, 10, 6] == 0 && DigitCount[#, 10, 7] == 0 &]

primes_with(, 1, [0, 1, 2, 3, 4, 5, 8, 9]) \\ uses function in A385776

print(list(islice(primes_with("01234589"), 41))) # uses function/imports in A385776

A386004 Primes whose digit set intersects the odd digits in at most one element and intersects the even digits in at most two elements.

Original entry on oeis.org

2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 181, 211, 223, 227, 229, 233, 241, 263, 269, 277, 281, 283, 383, 401, 409, 421, 433, 443, 449, 461, 463, 467, 487, 499, 601, 607, 641, 643, 647, 661, 677, 683, 727, 787, 809, 811, 821, 823, 827, 829, 863

Offset: 1

Jean-Marc Rebert, Jul 14 2025

From David A. Corneth, Jul 14 2025: (Start)
Terms can have at most three distinct digits.
Terms > 5 cannot have a digit 5. Proof: Terms > 5 are odd as they are prime. They cannot have a last digit 5. So if they have a digit 5 then they have at least two distinct odd digits contradicting the sequence definition of having at most one odd digit. (End)

			101 is a term because it is prime and its digit set is {0, 1} — containing at most one odd digit and no more than two distinct even digits.
1021 is a term because it is prime and its digit set is {0,1,2} — containing at most one odd digit and no more than two distinct even digits.

Cf. A000040, A020469, A020450, A020457, A020460, A385770.

Select[Prime[Range[150]],Length[Intersection[d=IntegerDigits[#],{1,3,5,7,9}]]<=1 && Length[Intersection[d,{0,2,4,6,8}]]<=2 &] (* Stefano Spezia, Jul 14 2025 *)

is(n) = if(!isprime(n), return(0)); my(s=Set(digits(n)), odd=0); if(#s>3,return(0)); odd=sum(i=1, #s ,bitand(s[i], 1)); if(odd > 1, return(0)); if(#s-odd > 2, return(0)); 1 \\ David A. Corneth, Jul 14 2025

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A174844 Primes that generate three other primes when 2, 6, and 8, respectively, are subtracted from each digit of their decimal representations.

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A386354 Primes without {6, 7} as digits.

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Magma

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A386004 Primes whose digit set intersects the odd digits in at most one element and intersects the even digits in at most two elements.

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Author

Keywords

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Programs

Mathematica

PARI