A052017 -id:A052017 - cp's OEIS frontend

A006055 Primes with consecutive (ascending) digits.

2, 3, 5, 7, 23, 67, 89, 4567, 78901, 678901, 23456789, 45678901, 9012345678901, 789012345678901, 56789012345678901234567890123, 90123456789012345678901234567, 678901234567890123456789012345678901

Offset: 1

N. J. A. Sloane, Richard C. Schroeppel

J. S. Madachy, Consecutive-digit primes - again, J. Rec. Math., 5 (No. 4, 1972), 253-254.
Thomas E. Moore, A Note on the Distribution of Primes in Arithmetic Progressions, J. Rec. Math., 5 (1972), 253-254.
R. C. Schroeppel, personal communication, 1991.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Zwillinger, Consecutive-Digit Primes - In Different Bases, J. Rec. Math., 10 (1972), 32-33.

Paul Tek, Table of n, a(n) for n = 1..36
J. S. Madachy, Consecutive-digit primes - again, J. Rec. Math., 5 (No. 4, 1972), 253-254. (Annotated scanned copy with letter to N. J. A. Sloane)
R. Schroeppel, Email to N. J. A. Sloane, Jun 1991
R. Schroeppel, Email to N. J. A. Sloane, Jun. 1991
Eric Weisstein's World of Mathematics, Prime Number.

Cf. A052016, A052017, A048398, A120804, A120805.

f[n_] := Block[{u = Range@n, t = Table[1, {n}]}, Select[ Drop[ Union@ Flatten@ Table[ FromDigits[ Mod[u + i*t, 10]], {i, 10}], 2], PrimeQ@# &]]; Array[f, 35] // Flatten (* Robert G. Wilson v, Jul 05 2006 *)

from sympy import isprime
from itertools import count, islice
def bgen(): yield from (int("".join(str((s0+i)%10) for i in range(d))) for d in count(1) for s0 in range(1, 10))
def agen(): yield from filter(isprime, bgen())
print(list(islice(agen(), 18))) # Michael S. Branicky, May 26 2022

a(17) from Robert G. Wilson v, Jul 05 2006

Entry revised by N. J. A. Sloane, Feb 07 2007

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} &]

A071363 Largest n-digit prime with strictly increasing digits.

Original entry on oeis.org

7, 89, 569, 5689, 34679, 345689, 1456789, 23456789

Offset: 1

Rick L. Shepherd, May 21 2002

Notice the terms with consecutive digits; search for 23456789 to find several related sequences including A006055, A052017 and A052077.

			a(1) = A052015(4), a(2) = A052015(15), a(3) = A052015(35), a(4) = A052015(61), ... In short, a(n) = A052015(b(n)) with b = (4, 15, 35, 61, 81, 94, 98, 100). - _M. F. Hasler_, May 03 2017

Cf. A071362, A071360, A071361, A007810.

Subsequence of A052015.

A071363(n,u=vectorv(n,i,10^(n-i)))={forvec(d=vector(n,i,[1,9]),isprime(d*u)&&n=d*u,2);n} \\ M. F. Hasler, May 03 2017

A138141 Numbers with digits in ascending order that differ exactly by 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 23, 34, 45, 56, 67, 78, 89, 123, 234, 345, 456, 567, 678, 789, 1234, 2345, 3456, 4567, 5678, 6789, 12345, 23456, 34567, 45678, 56789, 123456, 234567, 345678, 456789, 1234567, 2345678, 3456789, 12345678, 23456789, 123456789

Offset: 1

Omar E. Pol, Mar 19 2008

This finite sequence has 45 members. The last member is 123456789. There are 10-k members with k digits. See A052017 for primes in this sequence. All members with 3 or more digits are straight-line numbers A135643.

Cf. A052017, A059043, A135643, A138142.

Table[FromDigits/@Partition[Range[9],n,1],{n,9}]//Flatten (* Harvey P. Dale, Mar 19 2017 *)

a(n) = floor(((9*t^2 - 189*t + 18*n + 182) * (10^t - 1) - 18*t) / 162), where t = floor((21 - sqrt(369 - 8*n)) / 2). - Christopher J. Thomas, Feb 14 2024

A052016 Primes with digits in descending order that differ exactly by 1.

Original entry on oeis.org

2, 3, 5, 7, 43, 76543

Offset: 1

Patrick De Geest, Nov 15 1999

Primes in A138142. - Omar E. Pol, Dec 07 2008

Cf. A052017, A048398, A006055, A138142.

fQ[n_]:=Module[{id=IntegerDigits[n],}, n < 10 || Union[Differences[id]] == {-1}]; Select[Prime[Range[10000]], fQ] (* Vladimir Joseph Stephan Orlovsky, Dec 29 2010 *)

A058024 a(n) = A051451(n) - A058023(n).

Original entry on oeis.org

3, 5, 7, 11, 11, 17, 19, 23, 17, 43, 59, 37, 29, 41, 53, 43, 37, 43, 47, 83, 71, 83, 61, 149, 73, 97, 89, 109, 113, 103, 113, 89, 137, 167, 157, 181, 239, 139, 241, 139, 179, 233, 193, 163, 241, 173, 283, 167, 271, 193, 277, 181, 179, 199, 269, 193, 223, 239

Offset: 3

Labos Elemer, Nov 15 2000

nonn

			So far, all terms are primes. The analogy with fortunate numbers (A005235) is clear.

Sean A. Irvine, Table of n, a(n) for n = 3..256

Cf. A000961, A003418, A005235, A051451, A052017, A055211, A057034.

Edited by N. J. A. Sloane, Aug 20 2021

Name corrected by Sean A. Irvine, Jul 18 2022

cp's OEIS Frontend

A006055 Primes with consecutive (ascending) digits.

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A048398 Primes with consecutive digits that differ exactly by 1.

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A071363 Largest n-digit prime with strictly increasing digits.

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A138141 Numbers with digits in ascending order that differ exactly by 1.

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A052016 Primes with digits in descending order that differ exactly by 1.

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A058024 a(n) = A051451(n) - A058023(n).

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