A006055 Primes with consecutive (ascending) digits. (Formerly M0679)

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

Offset

1,1

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A056041 A083017 A006510 * A052017 A355804 A277575

Adjacent sequences: A006052 A006053 A006054 * A006056 A006057 A006058

Keyword

nonn,base

Author

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

Extensions

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

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

Status

approved