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
Links
- 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
Crossrefs
Programs
-
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
-
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
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
Comments