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

Author

T. D. Noe, Feb 11 2008

Keywords

• base
• fini
• nonn

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

Examples

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

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

Crossrefs

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

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

Programs

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

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