A182781 - OEIS

%I #36 Jun 05 2017 19:01:06

%S 4,4,2,1,12,20,35,28,80,114,211,228,736,1214,2101,2536,7799,13830,

%T 22107,27265,82611,144324,259260,354029,901774,1651718,2913981,

%U 3913728,11048656,19782855,33483206,49533124

%N Number of n-digit terms in A048398.

%C Also, number of n-digit primes in A033075.

%C Appears to be strictly increasing for n >= 8. - _Chai Wah Wu_, May 31 2017

%p A182781aux := proc(Lhig,n) local lsb,a ; if n = 0 then if isprime(Lhig) then    1; else 0; end if; else a := 0 ; lsb := Lhig mod 10 ; if lsb > 0 then a := a + procname(10*Lhig+lsb-1,n-1) ; end if; if lsb < 9 then a := a + procname(10*Lhig+lsb+1,n-1) ; end if; a; end if; end proc:

%p A182781 := proc(n) if n = 1 then 4; else a := 0 ; for l from 1 to 9 do a := a + A182781aux(l,n-1) ; end do: a ; end if; end proc: # _R. J. Mathar_, Feb 01 2011

%o (Python 3.2 or higher)

%o from itertools import product, accumulate

%o from sympy import isprime

%o def A182781(n):

%o     if n == 1:

%o         return 4

%o     count = 0

%o     for d in [1,3,7,9]:

%o         for elist in product([-1,1],repeat=n-1):

%o             flist = [str(x) for x in accumulate([d]+list(elist)) if 0 <= x < 10]

%o             if len(flist) == n and flist[-1] != '0' and is_prime(int(''.join(flist[::-1]))):

%o                 count += 1

%o     return count # _Chai Wah Wu_, Jun 05 2017

%Y Cf. A033075, A048398.

%K nonn,base,more

%O 1,1

%A _Zak Seidov_, Feb 01 2011

%E a(22)-a(24) from _Chai Wah Wu_, May 31 2017

%E a(25)-a(32) from _Chai Wah Wu_, Jun 05 2017