A120805 -id:A120805 - 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

A120804 Primes with consecutive digits descending.

Original entry on oeis.org

2, 3, 5, 7, 43, 109, 10987, 76543, 10987654321098765432109876543210987, 4321098765432109876543210987654321098765432109876543210987654321

Offset: 1

Robert G. Wilson v, Jul 05 2006

Digits can be in descending order. After 0 comes 9.

a(15) has 1053 digits. - Michael S. Branicky, Aug 05 2022

Paul Tek, Table of n, a(n) for n = 1..14

Cf. A006055, A120805.

f[n_] := Block[{d = Reverse@ Range@n, t = Table[1, {n}]}, Select[ Drop[ Union@ Flatten@ Table[ FromDigits[ Mod[d + i*t, 10]], {i, 10}], 2], PrimeQ@# &]]; Array[f, 1000] // Flatten

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(), 10))) # Michael S. Branicky, Aug 05 2022

Corrected by Paul Tek, May 08 2013

cp's OEIS Frontend

A006055 Primes with consecutive (ascending) digits.

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