A006055 -id:A006055 - cp's OEIS frontend

A006510 Duplicate of A006055.

Original entry on oeis.org

2, 3, 5, 7, 23, 67, 89, 4567, 78901, 678901, 23456789, 45678901, 9012345678901

Offset: 1

N. J. A. Sloane, Jun 13 2012

dead

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A048398 Primes with consecutive digits that differ exactly by 1.

Original entry on oeis.org

2, 3, 5, 7, 23, 43, 67, 89, 101, 787, 4567, 12101, 12323, 12343, 32321, 32323, 34543, 54323, 56543, 56767, 76543, 78787, 78989, 210101, 212123, 234323, 234343, 432121, 432323, 432343, 434323, 454543, 456767, 654323, 654343, 678767, 678989

Offset: 1

Patrick De Geest, Apr 15 1999

Or, primes in A033075. - Zak Seidov, Feb 01 2011

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 67, p. 23, Ellipses, Paris 2008.

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..1500 from Zak Seidov)

Cf. A033075, A048399-A048405, A052016, A052017, A006055.

Cf. A010051; intersection of A033075 and A000040.

a048398 n = a048398_list !! (n-1)
a048398_list = filter ((== 1) . a010051') a033075_list
-- Reinhard Zumkeller, Feb 21 2012, Nov 04 2010
(Python 3.2 or higher)
from itertools import product, accumulate
from sympy import isprime
A048398_list = [2,3,5,7]
for l in range(1,17):
    for d in [1,3,7,9]:
        dlist = [d]*l
        for elist in product([-1,1],repeat=l):
            flist = [str(d+e) for d,e in zip(dlist,accumulate(elist)) if 0 <= d+e < 10]
            if len(flist) == l and flist[-1] != '0':
                n = 10*int(''.join(flist[::-1]))+d
                if isprime(n):
                    A048398_list.append(n)
A048398_list = sorted(A048398_list) # Chai Wah Wu, May 31 2017

Select[Prime[Range[10000]], # < 10 || Union[Abs[Differences[IntegerDigits[#]]]] == {1} &]

A120819 Indices of primes in A057137.

Original entry on oeis.org

171, 277, 367, 561, 567, 18881

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 1 and after 9 comes 0.
Indices of primes in A057137.
All terms must end in 1 or 7: A057137(n) is even when n is even, and divisible by 3 iff n == 0, 2, 3, 5, 6, 8 or 9 (mod 10). - M. F. Hasler, Apr 14 2024
a(7) >= 100000. - Michael S. Branicky, Apr 07 2025

			a(1) = 12345678901234567890...01234567890...012345678901 = A057137(171) is the first prime term in A057137.

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61, 298.

Cf. A006055, A057137, A120828, A120820, A120821, A120822, A120823, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst
IntegerLength[Select[Table[FromDigits[PadRight[{},n,{1,2,3,4,5,6,7,8,9,0}]],{n,1,1001,2}],PrimeQ]] (* Harvey P. Dale, Feb 07 2024 *)

N=0;for(n=1,600,if(ispseudoprime(N=10*N+n%10),print1(n", "))) \\ Charles R Greathouse IV, May 10 2014  (Comment: Surprisingly, this is faster than calling ispseudoprime() only when n ends in 1 or 7, even when much larger N's are considered, e.g., up to 3000. - M. F. Hasler, Apr 14 2024)

from sympy import isprime
L = ['8901', '234567']; s = '1234567'; c = len(s); m = 0
while c < 18881:
    s += L[m%2]; c = len(s); m += 1
    if isprime(int(s)): print(c, end = ', ')  # Ya-Ping Lu, Jan 24 2025

a(6) from Arjen Lenstra, Feb 20 2012

A120821 a(n) consecutive digits ascending beginning with the digit 3 give a prime.

Original entry on oeis.org

1, 179, 529, 62625

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 3 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 3 give a prime." has only one term, 1 which represents the prime 3.
a(5) > 10^5. - Michael S. Branicky, Apr 08 2025

Cf. A006055, A120819, A120820, A120822, A120823, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[2+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

a(4) from Michael S. Branicky, Apr 03 2025

A120822 a(n) consecutive digits ascending beginning with the digit 4 give a prime.

Original entry on oeis.org

4, 8, 194

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 4; after 9 comes 0.

a(4) > 10^5. - Michael S. Branicky, Apr 08 2025

			8 is a term since 45678901 is a prime.

Cf. A006055, A120829, A120819, A120820, A120821, A120823, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[3+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

A120820 a(n) consecutive digits ascending beginning with the digit 2 give a prime.

Original entry on oeis.org

1, 2, 8, 82, 118, 158, 2122, 2242, 2388

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 2 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 2 give a prime" has only one term, 1 which represents the prime 2.
a(10) > 10^5. - Michael S. Branicky, Apr 10 2025

			8 is a term since 23456789 is a prime.

Cf. A006055, A120819, A120821, A120822, A120823, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[1+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

A120823 a(n) consecutive digits ascending beginning with the digit 5 give a prime..

Original entry on oeis.org

1, 29, 269, 689

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 5 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 5 give a prime." has only one term, 1 which represents the prime 5.
a(5) > 10^5. - Michael S. Branicky, Apr 08 2025

			29 is a term since the 29-digit number 56789012345678901234567890123 is a prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120824, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[4+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 9000}]; lst

A120824 a(n) consecutive digits ascending beginning with the digit 6 give a prime.

Original entry on oeis.org

2, 6, 36, 122, 336, 82812

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 6 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 6 give a prime" has no terms.
a(7) >= 100000. - Michael S. Branicky, Apr 07 2025

			6 is a term since 678901 is a prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120825, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[5+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

a(6) from Michael S. Branicky, Apr 05 2025

A120825 a(n) consecutive digits ascending beginning with the digit 7 give a prime.

Original entry on oeis.org

1, 5, 15, 51, 8411

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 7 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 7 give a prime" has only two terms below 6001, namely 1 and 5, which represent the primes 7 and 76543, respectively.
a(6) >= 100000. - Michael S. Branicky, Apr 07 2025

			1 is here because 7 is prime.
5 is here because 78901 is prime.
15 is here because 789012345678901 is a prime.
51 is here because 789012345678901234567890123456789012345678901234567 is prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120824, A120826, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[6+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

a(5) from Bert Dobbelaere, Apr 01 2025

A120826 a(n) consecutive digits ascending beginning with the digit 8 give a prime.

Original entry on oeis.org

2, 82, 152, 7066, 84892

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits are in ascending order beginning with 8 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 8 give a prime" has no terms.
a(6) > 10^5. - Michael S. Branicky, Apr 11 2025

			2 is a term since 89 is a prime.
82 is a term because 8901234567890123456789012345678901234567890123456789012345678901234567890123456789 is a prime.

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120824, A120825, A120827.

fQ[n_] := PrimeQ@ FromDigits@ Mod[7+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

a(4) from Bert Dobbelaere, Apr 01 2025

a(5) from Michael S. Branicky, Apr 03 2025

cp's OEIS Frontend

A006510 Duplicate of A006055.

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A048398 Primes with consecutive digits that differ exactly by 1.

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A120819 Indices of primes in A057137.

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A120821 a(n) consecutive digits ascending beginning with the digit 3 give a prime.

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A120822 a(n) consecutive digits ascending beginning with the digit 4 give a prime.

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A120820 a(n) consecutive digits ascending beginning with the digit 2 give a prime.

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A120823 a(n) consecutive digits ascending beginning with the digit 5 give a prime..

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A120824 a(n) consecutive digits ascending beginning with the digit 6 give a prime.

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A120825 a(n) consecutive digits ascending beginning with the digit 7 give a prime.

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