A050987 Number of n-digit left-truncatable primes.

4, 11, 39, 99, 192, 326, 429, 521, 545, 517, 448, 354, 276, 212, 117, 72, 42, 24, 13, 6, 5, 4, 3, 1, 0

Offset: 1

Author

Eric W. Weisstein

Keywords

• base
• nonn
• easy
• fini
• full

Comments

The sequence is well defined for any positive integer, with a(n) = 0 for n >= 25. But it makes sense to consider it to be full & finite. - M. F. Hasler, Nov 07 2018

Links

• I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
• P. De Geest, The list of 4260 left-truncatable primes
• Eric Weisstein's World of Mathematics, Truncatable Prime.
• Index entries for sequences related to numbers of primes in various ranges
• Index entries for sequences related to truncatable primes

Crossrefs

Cf. A033664, A024785, A032437, A020994, A024770, A052023, A052024, A052025, A050986.

Programs

PARI

A050987=vector(25, n, #p=concat(apply(p->select(isprime, vector(9, i, i*10^(n-1)+p)), if(n>1, p)))) \\ M. F. Hasler, Nov 07 2018

Python

from sympy import isprime
def alst():
  primes, alst = [2, 3, 5, 7], [4]
  while len(primes) > 0:
    candidates = set(int(d+str(p)) for p in primes for d in "123456789")
    primes = [c for c in candidates if isprime(c)]
    alst.append(len(primes))
  return alst
print(alst()) # Michael S. Branicky, Apr 11 2021

Extensions

Edited by Ray Chandler, Mar 13 2007

a(25) = 0 added by M. F. Hasler, Nov 07 2018