A076623 Total number of left truncatable primes (without zeros) in base n.

0, 3, 16, 15, 454, 22, 446, 108, 4260, 75, 170053, 100, 34393, 9357, 27982, 362, 14979714, 685, 3062899, 59131, 1599447, 1372, 1052029701, 10484, 7028048, 98336, 69058060, 3926

Offset

2,2

Comments

Approximation of a(b) by (PARI) code: l(b)=c=b*(b-1)/log(b)/eulerphi(b);\ return(floor((primepi(b)-omega(b))*exp(c)/c)); - Robert Gerbicz, Nov 02 2008

a(24) = 1052029701 based on strong BPSW pseudoprimes. Other terms up to a(29) use proved primes. - Martin Fuller, Nov 24 2008

Links

Table of n, a(n) for n=2..29.

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

Michael S. Branicky, String-based Python Program

Martin Fuller, Table of n, a(n) for n= 2..53, with question marks where unknown

Hans Havermann, A076623 Decomposed

Index entries for sequences related to truncatable primes

Maple

Lton := proc(L, b) add( op(i, L)*b^(i-1), i=1..nops(L)) ; end proc:
A076623rec := proc(L, b) local a, d, Lext, p ; a := 0 ; for d from 1 to b-1 do Lext := [op(L), d] ; p := Lton(Lext, b) ; if isprime(p) then a := a+1 ;  a := a+procname(Lext, b) ; end if; end do: a ; end proc:
A076623 := proc(b) A076623rec([], b) ; end proc:
for b from 2 do print(b, A076623(b)) ; end do: # R. J. Mathar, Jun 01 2011

Prog

(PARI)
f(b)=ct=0; A=[0]; n=-1; L=1; while(L, n++; B=vector(L*b); M=0; \
for(i=1, L, for(j=1, b-1, x=A[i]+j*b^n; if(isprime[x], M++; B[M]=x; ct++))); \
L=M; A=vector(L, i, B[i])); return(ct) \\ Robert Gerbicz, Oct 31 2008
(Python) # works for all n; link has faster string-based version for n < 37
from sympy import isprime, primerange
from sympy.ntheory.digits import digits
def fromdigits(digs, base):
    return sum(d*base**i for i, d in enumerate(digs))
def a(n):
    prime_lists, an = [(p, ) for p in primerange(1, n)], 0
    while len(prime_lists) > 0:
        an += len(prime_lists)
        candidates = set(p+(d, ) for p in prime_lists for d in range(1, n))
        prime_lists = [c for c in candidates if isprime(fromdigits(c, n))]
    return an
print([a(n) for n in range(2, 12)]) # Michael S. Branicky, Apr 27 2022

Crossrefs

Cf. A024779, A024780, A024781, A024782, A024783, A024784, A024785, A076586, A103443, A103463.

Sequence in context: A213847 A195883 A272329 * A370978 A068516 A219508

Adjacent sequences: A076620 A076621 A076622 * A076624 A076625 A076626

Keyword

nonn,base,more

Author

Martin Renner, Oct 22 2002, Nov 03 2002, Sep 24 2007, Feb 20 2008, Apr 20 2008

Extensions

a(12) corrected from 170051 to 170053 by Martin Fuller, Oct 31 2008

a(18) corrected by Robert Gerbicz, Nov 02 2008

a(24)-a(29) from Martin Fuller, Nov 24 2008

Entries in a-file corrected by N. J. A. Sloane, Jun 02 2011

Status

approved