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

Author

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

Keywords

• nonn
• base

References

• 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.

Links

• 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.

Crossrefs

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

Programs

Mathematica

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 *)

Python

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

Extensions

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

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