A020455 -id:A020455 - cp's OEIS frontend

A276039 Numbers using only digits 1 and 7.

1, 7, 11, 17, 71, 77, 111, 117, 171, 177, 711, 717, 771, 777, 1111, 1117, 1171, 1177, 1711, 1717, 1771, 1777, 7111, 7117, 7171, 7177, 7711, 7717, 7771, 7777, 11111, 11117, 11171, 11177, 11711, 11717, 11771, 11777, 17111, 17117, 17171, 17177, 17711, 17717, 17771, 17777

Offset: 1

Vincenzo Librandi, Aug 19 2016

Numbers k such that the product of digits of k is a power of 7.

There are no prime terms whose number of digits is divisible by 3: for every d that is a multiple of 3, every d-digit number j consisting of no digits other than 1's and 7's will have a digit sum divisible by 3, so j will also be divisible by 3. - Mikk Heidemaa, Mar 27 2021

			7717 is in the sequence because 7*7*1*7 = 343 = 7^3.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. similar sequences listed in A276037.

Cf. A020455, A002275, A002281, A034054.

[n: n in [1..24000] | Set(Intseq(n)) subset {1,7}];

Select[Range[20000], IntegerQ[Log[7, Times@@(IntegerDigits[#])]] &] (* or *) Flatten[Table[FromDigits/@Tuples[{1, 7}, n], {n, 6}]]

is(n) = my(d=digits(n), e=[0, 2, 3, 4, 5, 6, 8, 9]); if(#setintersect(Set(d), Set(e))==0, return(1), return(0)) \\ Felix Fröhlich, Aug 19 2016

a(n) = { my(b = binary(n + 1)); b = b[^1]; b = apply(x -> 6*x + 1, b); fromdigits(b) } \\ David A. Corneth, Mar 27 2021

def a(n):
  b = bin(n+1)[3:]
  return int("".join(b.replace("1", "7").replace("0", "1")))
print([a(n) for n in range(1, 47)]) # Michael S. Branicky, Mar 27 2021

def A276039(n): return 6*int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1)//9 # Chai Wah Wu, Jun 28 2025

A260889 Primes having only {1, 2, 7} as digits.

Original entry on oeis.org

2, 7, 11, 17, 71, 127, 211, 227, 271, 277, 727, 1117, 1171, 1217, 1277, 1721, 1777, 2111, 2221, 2711, 2777, 7121, 7127, 7177, 7211, 7717, 7727, 11117, 11171, 11177, 11717, 11777, 12211, 12227, 12277, 12721, 17117, 21121, 21211, 21221, 21227, 21277, 21727

Offset: 1

Vincenzo Librandi, Aug 04 2015

A020450, A020455 and A020459 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Cf. Primes that contain only the digits (k,1,7): A199327 (k=0), this sequence (k=2), A260379 (k=3), A079651 (k=4), A260828 (k=5), A260891 (k=6), A260892 (k=8), A260893 (k=9).

Cf. A020450, A020455, A020459.

[p: p in PrimesUpTo(3*10^4) | Set(Intseq(p)) subset [1, 2, 7]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {1, 2, 7}] == {} &]
Table[Select[FromDigits/@Tuples[{1,2,7},n],PrimeQ],{n,5}]//Flatten (* Harvey P. Dale, Apr 12 2018 *)

A260828 Primes having only {1, 5, 7} as digits.

Original entry on oeis.org

5, 7, 11, 17, 71, 151, 157, 557, 571, 577, 751, 757, 1117, 1151, 1171, 1511, 1571, 1777, 5171, 5557, 5711, 5717, 7151, 7177, 7517, 7577, 7717, 7757, 11117, 11171, 11177, 11551, 11717, 11777, 15511, 15551, 17117, 17551, 51151, 51157, 51511, 51517, 51551, 51577

Offset: 1

Vincenzo Librandi, Aug 02 2015

Alois P. Heinz, Table of n, a(n) for n = 1..10000
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019)
Index to entries for primes with digits in a given set

Subsequence of A030096. A020453, A020455 and A020467 are subsequences.
Cf. similar sequences listed in A260827.
Cf. A000040.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1,5,7]];

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 5, 7}] == {} &]

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
  n, digits, alst = 0, 1, []
  while len(alst) < terms:
    mpstr = "".join(d*digits for d in "157")
    for mp in multiset_permutations(mpstr, digits):
      t = int("".join(mp))
      if isprime(t): alst.append(t)
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(44)) # Michael S. Branicky, May 07 2021

A260379 Primes having only {1, 3, 7} as digits.

Original entry on oeis.org

3, 7, 11, 13, 17, 31, 37, 71, 73, 113, 131, 137, 173, 311, 313, 317, 331, 337, 373, 733, 773, 1117, 1171, 1373, 1733, 1777, 3137, 3313, 3331, 3371, 3373, 3733, 7177, 7331, 7333, 7717, 11113, 11117, 11131, 11171, 11173, 11177, 11311, 11317, 11717, 11731, 11777

Offset: 1

Vincenzo Librandi, Jul 24 2015

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Subsequence of A030096 and A155055. A020451, A020455, and A020463 are subsequences.
Cf. similar sequences listed in A260378.
Cf. A000040, A020451, A020455, A020463.

[p: p in PrimesUpTo(2*10^4) | Set(Intseq(p)) subset [1, 3, 7]];

Select[Prime[Range[2 10^3]], Complement[IntegerDigits[#], {1, 3, 7}]=={} &]

A260891 Primes having only {1, 6, 7} as digits.

Original entry on oeis.org

7, 11, 17, 61, 67, 71, 167, 617, 661, 677, 761, 1117, 1171, 1667, 1777, 6661, 6761, 7177, 7717, 11117, 11161, 11171, 11177, 11617, 11677, 11717, 11777, 16111, 16661, 17117, 17167, 17761, 61667, 61717, 66161, 66617, 67777, 71161, 71167, 71171, 71671

Offset: 1

Vincenzo Librandi, Aug 05 2015

A020454, A020455 and A020469 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Cf, similar sequences listed in A260889.

Cf. A000040, A020454, A020455, A020469.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1, 6, 7]];

Select[Prime[Range[2 10^4]], Complement[IntegerDigits[#], {1, 6, 7}] == {} &]

A260892 Primes having only {1, 7, 8} as digits.

Original entry on oeis.org

7, 11, 17, 71, 181, 787, 811, 877, 881, 887, 1117, 1171, 1181, 1187, 1777, 1787, 1811, 1871, 1877, 7177, 7187, 7717, 7817, 7877, 8111, 8117, 8171, 8887, 11117, 11171, 11177, 11717, 11777, 11887, 17117, 17881, 18181, 18787, 71171, 71711, 71777, 71881, 71887

Offset: 1

Vincenzo Librandi, Aug 07 2015

A020455, A020456 and A020470 are subsequences.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Cf. similar sequences listed in A260889.

Cf. A000040, A020455, A020456, A020470.

[p: p in PrimesUpTo(2*10^5) | Set(Intseq(p)) subset [1, 7, 8]];

Select[Prime[Range[2 10^5]], Complement[IntegerDigits[#], {1, 7, 8}] == {} &]

A260893 Primes having only {1, 7, 9} as digits.

Original entry on oeis.org

7, 11, 17, 19, 71, 79, 97, 179, 191, 197, 199, 719, 797, 911, 919, 971, 977, 991, 997, 1117, 1171, 1777, 1979, 1997, 1999, 7177, 7717, 7919, 9199, 9719, 9791, 11117, 11119, 11171, 11177, 11197, 11717, 11719, 11777, 11779, 11971, 17117, 17191, 17791, 17911

Offset: 1

Vincenzo Librandi, Aug 11 2015

A020455, A020457 and A020471 are subsequences.

Subsequence of A030096.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Index to entries for primes with digits in a given set

Cf. similar sequences listed in A260889.

Cf. A000040, A020455, A020457, A020471, A030096.

[p: p in PrimesUpTo(3*10^4) | Set(Intseq(p)) subset [1, 7, 9]];

Select[Prime[Range[3 10^3]], Complement[IntegerDigits[#], {1, 7, 9}] == {}&]

A036307 Composite numbers whose prime factors contain no digits other than 1 and 7.

Original entry on oeis.org

49, 77, 119, 121, 187, 289, 343, 497, 539, 781, 833, 847, 1207, 1309, 1331, 2023, 2057, 2401, 3179, 3479, 3773, 4913, 5041, 5467, 5831, 5929, 7819, 8197, 8449, 8591, 9163, 9317, 12287, 12439, 12881, 13277, 14161, 14399, 14641, 16807, 18989, 19547

Offset: 1

Patrick De Geest, Dec 15 1998

All terms are a product of at least two terms of A020455. - David A. Corneth, Oct 09 2020

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Alois P. Heinz)
Index entries for sequences related to prime factors.

Cf. A003599, A020455, A036302-A036325.

Sum_{n>=1} 1/a(n) = Product_{p in A020455} (p/(p - 1)) - Sum_{p in A020455} 1/p - 1 = 0.0775663737... . - Amiram Eldar, May 18 2022

A036934 Smallest n-digit prime containing only digits 1 and 7, or 0 if no such prime exists.

Original entry on oeis.org

7, 11, 0, 1117, 11117, 0, 1111711, 11111117, 0, 1111117171, 11111111771, 0, 1111111111177, 11111111171177, 0, 1111111111171177, 11111111111111171, 0, 1111111111111111111, 11111111111111117111, 0, 1111111111111111111711

Offset: 1

Patrick De Geest, Jan 04 1999

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Cf. A020455, A036307, A036229.

Flatten[Table[Select[FromDigits/@Tuples[{1, 7}, n], PrimeQ, 1], {n, 25}]/.{}->{0}] (* Jinyuan Wang, Mar 09 2020 *)

a(16) corrected by Jinyuan Wang, Mar 09 2020

A358020 Least prime number > prime(n) (n >= 5) whose set of decimal digits coincides with the set of decimal digits of prime(n), or -1 if no such prime exists.

Original entry on oeis.org

1111111111111111111, 31, 71, 191, 223, 229, 113, 73, 4111, 433, 4447, 353, 599, 661, 677, 1117, 337, 97, 383, 8999, 797, 10111, 1013, 701, 1009, 131, 271, 311, 173, 193, 419, 1151, 571, 613, 617, 317, 197, 811, 199, 1193, 719, 911, 2111, 233, 277, 929, 2333, 293, 421, 521, 2557

Offset: 5

Jean-Marc Rebert, Oct 24 2022

			prime(6) = 13 and the prime number 31 have the same set of digits {1,3}, and 31 is the smallest such number, hence a(6) = 31.
prime(13) = 41 and the prime number 4111 have the same set of digits {1,4}, and 4111 is the smallest such number, hence a(13) = 4111.
prime(20) = 71 and the prime number 1117 have the same set of digits {1,7}, and 1117 is the smallest such number, hence a(20) = 1117.

Jean-Marc Rebert, Table of n, a(n) for n = 5..10000

Cf. A000040, A357096, A004022, A004023, A020451, A020455, A050288, A166681.

N:= 60: # for a(5)..a(N)
A:= Array(5..N):
R:= 1111111111111111111:
A[5]:= R: count:= 1:
for k from 6 while count < N-4 do
  p:= ithprime(k);
  S:= convert(convert(p,base,10),set);
  if assigned(V[S]) and V[S]<=N then A[V[S]]:= p; count:=count+1;  fi;
  V[S]:= k;
od:
convert(A,list); # Robert Israel, Oct 25 2022

a(n)=my(m=Set(digits(prime(n)))); if(n<5, return()); if(n==5,return(1111111111111111111));forprime(p=prime(n+1), , if(Set(digits(p))==m, return(p)))

from sympy import isprime, prime
from itertools import count, product
def a(n):
    pn = prime(n)
    s = str(pn)
    for d in count(len(s)):
        for p in product(set(s), repeat=d):
            if p[0] == "0": continue
            t = int("".join(p))
            if t > pn and isprime(t):
                return t
print([a(n) for n in range(5, 56)]) # Michael S. Branicky, Oct 25 2022

cp's OEIS Frontend

A276039 Numbers using only digits 1 and 7.

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A260889 Primes having only {1, 2, 7} as digits.

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A260828 Primes having only {1, 5, 7} as digits.

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A260379 Primes having only {1, 3, 7} as digits.

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A260891 Primes having only {1, 6, 7} as digits.

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A260892 Primes having only {1, 7, 8} as digits.

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A260893 Primes having only {1, 7, 9} as digits.

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A036307 Composite numbers whose prime factors contain no digits other than 1 and 7.

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