A030432 -id:A030432 - cp's OEIS frontend

A181605 Twin primes ending in 7.

7, 17, 107, 137, 197, 227, 347, 617, 827, 857, 1277, 1427, 1487, 1607, 1667, 1697, 1787, 1877, 1997, 2027, 2087, 2237, 2267, 2657, 2687, 3167, 3257, 3467, 3527, 3557, 3767, 3917, 4127, 4157, 4217, 4337, 4517, 4547, 4637, 4787, 4967, 5417, 5477, 5657

Offset: 1

Omar E. Pol, Nov 01 2010

First disagrees with A092340 at n=26: A092340 contains 2707, but this sequence doesn't. Is this a subsequence of A092340? - Nathaniel Johnston, Jun 25 2011

Yes, it is a subsequence of A092340: see link. - Robert Israel, Apr 13 2021

Robert Israel, Table of n, a(n) for n = 1..10000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
Robert Israel, A181605 is a subsequence of A092340

Cf. A001097, A092340, A181603, A181604, A181606.

[7, op(select(t -> isprime(t) and isprime(t+2), [seq(i,i=17..10000,30)]))]; # Robert Israel, Apr 13 2021

Select[Prime@ Range@ 800, Mod[ #, 10] == 7 && (PrimeQ[ # - 2] || PrimeQ[ # + 2]) &] (* Robert G. Wilson v, Nov 06 2010 *)

A001097 INTERSECT A030432. - R. J. Mathar, Nov 03 2010

More terms from R. J. Mathar and Robert G. Wilson v, Nov 03 2010

A045380 Primes congruent to 2 mod 5.

Original entry on oeis.org

2, 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577, 587, 607, 617, 647, 677, 727, 757, 787, 797, 827, 857, 877, 887, 907, 937, 947, 967, 977, 997, 1087, 1097, 1117, 1187, 1217, 1237

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Apart from the initial terms, essentially same as A030432 and A045357. Cf. A095022.

[p: p in PrimesUpTo(1300) | p mod 5 eq 2]; // Vincenzo Librandi, Aug 07 2012

Select[Prime@Range[210], Mod[ #, 5] == 2 &] (* Ray Chandler, Dec 06 2006 *)
Select[Range[2,1300,5],PrimeQ] (* Harvey P. Dale, Jul 22 2020 *)

is(n)=isprime(n) && n%5==2 \\ Charles R Greathouse IV, Jul 01 2016

A385770 Primes having only {0, 6, 7} as digits.

Original entry on oeis.org

7, 67, 607, 677, 6007, 6067, 6607, 7607, 60077, 60607, 66067, 67607, 67777, 70067, 70607, 70667, 76607, 76667, 76777, 606077, 606607, 607007, 607067, 607667, 660067, 660607, 666067, 666607, 666667, 666707, 670777, 676007, 677077, 677767, 700067

Offset: 1

Jason Bard, Jul 09 2025

			6007 is a term because it is prime and has only {0,6,7} as digits.

Subsequence of A030432.

Cf. A000040, A020469, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [0, 6, 7]];

Select[FromDigits/@Tuples[{0,6,7},5],PrimeQ]

primes_with(, 1, [0, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("067"), 41))) # uses function/imports in A385776

A385784 Primes having only {2, 4, 7} as digits.

Original entry on oeis.org

2, 7, 47, 227, 277, 727, 2447, 2477, 2777, 4447, 7247, 7477, 7727, 22247, 22277, 22447, 22727, 22777, 24247, 27277, 27427, 42227, 42727, 44777, 47777, 72227, 72277, 72727, 74747, 77447, 77477, 77747, 222247, 242227, 242447, 242747, 244247, 244747, 272227

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020459, A020465.

Cf. A000040, A030432, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 4, 7]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 4, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 4, 7]) \\ uses function in A385776

print(list(islice(primes_with("247"), 41))) # uses function/imports in A385776

A385787 Primes having only {2, 6, 7} as digits.

Original entry on oeis.org

2, 7, 67, 227, 277, 677, 727, 2267, 2677, 2767, 2777, 6277, 7727, 22277, 22727, 22777, 26227, 26267, 26627, 26777, 27277, 27767, 62627, 67777, 72227, 72277, 72727, 72767, 76667, 76777, 77267, 226267, 226777, 227267, 227627, 262627, 266677, 266767, 267227

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020459, A020469.

Cf. A000040, A030432, A385776.

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

Flatten[Table[Select[FromDigits /@ Tuples[{2, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("267"), 41))) # uses function/imports in A385776

A385789 Primes having only {2, 7, 8} as digits.

Original entry on oeis.org

2, 7, 227, 277, 727, 787, 827, 877, 887, 2287, 2777, 2887, 7727, 7877, 8287, 8887, 22277, 22727, 22777, 22787, 22877, 27277, 27827, 28277, 72227, 72277, 72287, 72727, 78277, 78787, 78877, 78887, 82727, 82787, 87277, 87877, 87887, 222787, 222877, 227827, 228887

Offset: 1

Jason Bard, Jul 13 2025

Supersequence of A020459, A020470.

Cf. A000040, A030432, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [2, 7, 8]];

Flatten[Table[Select[FromDigits /@ Tuples[{2, 7, 8}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [2, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("278"), 41))) # uses function/imports in A385776

A385794 Primes having only {4, 6, 7} as digits.

Original entry on oeis.org

7, 47, 67, 467, 647, 677, 4447, 7477, 44647, 44777, 46447, 46477, 46747, 47777, 64667, 64747, 66467, 67447, 67477, 67777, 74747, 76667, 76777, 77447, 77477, 77647, 77747, 444677, 444767, 446447, 446477, 446647, 446767, 447467, 447677, 464447, 464467, 464647, 464747

Offset: 1

Jason Bard, Jul 13 2025

Subsequence of A030432.
Supersequence of A020465, A020469.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 6, 7]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 6, 7}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 6, 7]) \\ uses function in A385776

print(list(islice(primes_with("467"), 41))) # uses function/imports in A385776

A385795 Primes having only {4, 7, 8} as digits.

Original entry on oeis.org

7, 47, 487, 787, 877, 887, 4447, 4787, 4877, 7477, 7487, 7877, 8447, 8747, 8887, 44777, 44887, 47777, 48487, 48787, 48847, 74747, 74887, 77447, 77477, 77747, 78487, 78787, 78877, 78887, 84787, 87877, 87887, 88747, 444487, 444877, 444887, 447877, 474787, 474847

Offset: 1

Jason Bard, Jul 13 2025

Subsequence of A030432.
Supersequence of A020465, A020470.
Cf. A000040, A385776.

[p: p in PrimesUpTo(10^6) | Set(Intseq(p)) subset [4, 7, 8]];

Flatten[Table[Select[FromDigits /@ Tuples[{4, 7, 8}, n], PrimeQ], {n, 7}]]

primes_with(, 1, [4, 7, 8]) \\ uses function in A385776

print(list(islice(primes_with("478"), 41))) # uses function/imports in A385776

A045357 Primes congruent to {0, 2} mod 5.

Original entry on oeis.org

2, 5, 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577, 587, 607, 617, 647, 677, 727, 757, 787, 797, 827, 857, 877, 887, 907, 937, 947, 967, 977, 997, 1087, 1097, 1117, 1187, 1217

Offset: 1

N. J. A. Sloane

Equivalently, primes congruent to {2,5,7} mod 10. [Bruno Berselli, Aug 07 2012]

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Apart from the initial terms essentially same as A030432 and A045380.

[ p: p in PrimesUpTo(2000) | p mod 5 in {0, 2} ]; // Vincenzo Librandi, Aug 07 2012

Select[Prime@Range[210], MemberQ[{0, 2}, Mod[ #, 5]] &] (* Ray Chandler, Jun 29 2008 *)

Extended by Ray Chandler, Nov 07 2006

A384449 Primes having only {0, 4, 7} as digits.

Original entry on oeis.org

7, 47, 4007, 4447, 7477, 44777, 47407, 47777, 74047, 74077, 74707, 74747, 77047, 77447, 77477, 77747, 407047, 407707, 407747, 440047, 444007, 444047, 470077, 470447, 474077, 474707, 477047, 477077, 704447, 704477, 704747, 704777, 707407, 707747, 740477, 744077, 744407, 744707, 747407, 770047

Offset: 1

Jason Bard, May 29 2025

Subsequence of A030432.
Supersequence of A020465.
Cf. Primes that contain only the digits (0,k,7): A199327 (k=1), A261267 (k=2), A260378 (k=3), this sequence (k=4), A260827 (k=5), A261181 (k=9).
Cf. A000040.

[p: p in PrimesUpTo(2*10^6) | Set(Intseq(p)) subset [0, 4, 7]];

Select[FromDigits/@Tuples[{0, 4, 7}, 6], PrimeQ]

from sympy import sieve
A384449 = [p for p in sieve.primerange(10**6) if all(n in ['0','4','7'] for n in str(p))] # Jwalin Bhatt,  Jun 02 2025

from itertools import count, islice
from gmpy2 import digits, is_prime
def A384449_gen(): # generator of terms
    for i in count(1):
        if is_prime(m:=int(digits(i,3).replace('1','4').replace('2','7'))):
            yield m
A384449_list = list(islice(A384449_gen(),40)) # Chai Wah Wu, Jun 07 2025

cp's OEIS Frontend

A181605 Twin primes ending in 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A045380 Primes congruent to 2 mod 5.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A385770 Primes having only {0, 6, 7} as digits.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A385784 Primes having only {2, 4, 7} as digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A385787 Primes having only {2, 6, 7} as digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A385789 Primes having only {2, 7, 8} as digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A385794 Primes having only {4, 6, 7} as digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Python

A385795 Primes having only {4, 7, 8} as digits.