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A137812
Left- or right-truncatable primes.
11
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
I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
Carlos Rivera, Puzzle 2: Prime Strings, The Prime Puzzles and Problems Connection.
Daniel Starodubtsev, Full sequence
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
KEYWORD
base,fini,nonn
AUTHOR
T. D. Noe, Feb 11 2008
STATUS
approved