A137812 Left- or right-truncatable primes.

2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 113, 131, 137, 139, 167, 173, 179, 197, 223, 229, 233, 239, 271, 283, 293, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 431, 433, 439, 443, 467, 479, 523, 547, 571

Offset

1,1

Comments

Repeatedly removing a digit from either the left or right produces only primes. There are 149677 terms in this sequence, ending with 8939662423123592347173339993799.

The number of n-digit terms is A298048(n). - Jon E. Schoenfield, Jan 28 2022

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.

T. D. Noe, Plot of all terms

Carlos Rivera, Puzzle 2: Prime Strings, The Prime Puzzles and Problems Connection.

Daniel Starodubtsev, Full sequence

Eric Weisstein, MathWorld: Truncatable Prime

Index entries for sequences related to truncatable primes

Example

139 is here because (removing 9 from the right) 13 is prime and (removing 1 from the left) 3 is prime.

Mathematica

Clear[s]; s[0]={2, 3, 5, 7}; n=1; While[s[n]={}; Do[k=s[n-1][[i]]; Do[p=j*10^n+k; If[PrimeQ[p], AppendTo[s[n], p]], {j, 9}]; Do[p=10*k+j; If[PrimeQ[p], AppendTo[s[n], p]], {j, 9}], {i, Length[s[n-1]]}]; s[n]=Union[s[n]]; Length[s[n]]>0, n++ ]; t=s[0]; Do[t=Join[t, s[i]], {i, n}]; t

Prog

(Python)
from sympy import isprime
def agen():
    primes = [2, 3, 5, 7]
    while len(primes) > 0:
        yield from primes
        cands = set(int(d+str(p)) for p in primes for d in "123456789")
        cands |= set(int(str(p)+d) for p in primes for d in "1379")
        primes = sorted(c for c in cands if isprime(c))
afull = [an for an in agen()]
print(afull[:60]) # Michael S. Branicky, Aug 04 2022

Crossrefs

Cf. A024770 (right-truncatable primes), A024785 (left-truncatable primes), A077390 (left-and-right truncatable primes), A080608.

Cf. A298048 (number of n-digit terms).

Sequence in context: A080608 A305352 A347864 * A216578 A094317 A074834

Adjacent sequences: A137809 A137810 A137811 * A137813 A137814 A137815

Keyword

base,fini,nonn

Author

T. D. Noe, Feb 11 2008

Status

approved