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A076623
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Total number of left truncatable primes (without zeros) in base n.
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14
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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
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OFFSET
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2,2
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COMMENTS
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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
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LINKS
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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
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MAPLE
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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
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PROG
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(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
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CROSSREFS
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Cf. A024779, A024780, A024781, A024782, A024783, A024784, A024785, A076586, A103443, A103463.
Sequence in context: A213847 A195883 A272329 * A068516 A219508 A032922
Adjacent sequences: A076620 A076621 A076622 * A076624 A076625 A076626
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KEYWORD
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nonn,base,more
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AUTHOR
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Martin Renner, Oct 22 2002, Nov 03 2002, Sep 24 2007, Feb 20 2008, Apr 20 2008
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EXTENSIONS
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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
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STATUS
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approved
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