A032734 All 81 combinations of prefixing and following a(n) by a single digit are nonprime.

2437, 5620, 7358, 11111, 13308, 13332, 13650, 14612, 19737, 19817, 24217, 25213, 26302, 27971, 28472, 28838, 29289, 29542, 29650, 31328, 33027, 33170, 35914, 35970, 36186, 37977, 38327, 39127, 39608, 40078, 41165, 41528, 42422, 43277, 44657, 45649, 47172, 47382

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for primes involving decimal expansion of n

Example

2437 prefixed and followed with a pair of digits from (1,2,3,4,5,6,7,8,9) never yields a prime, e.g., '9'2437'1' = 7 * 37 * 43 * 83.

Maple

isA032734 := proc(n)
        for k from 1 to 9 do
        for k2 from 1 to 9 do
                dgs := [k, op(convert(n, base, 10)), k2] ;
                dgsn := add( op(i, dgs)*10^(i-1), i=1..nops(dgs)) ;
                if isprime(dgsn) then
                        return false;
                end if;
        end do:
        end do:
        return true;
end proc:
for n from 1 to 50000 do
        if isA032734(n) then
                printf("%d, ", n);
        end if;
end do: # R. J. Mathar, Oct 22 2011
filter:= proc(n) local d, i, j;
     d:= 10^(ilog10(n)+2);
     not ormap(isprime, [seq(seq(d*i+10*n+j, j=[1, 3, 5, 7, 9]), i=1..9)])
end proc:
select(filter, [$1..10^5]); # Robert Israel, Jul 07 2016

Mathematica

ok[n_] := With[{id = IntegerDigits[n]}, Select[ Flatten[ Table[ FromDigits[ Join[{j}, id, {k}]], {j, 1, 9}, {k, 1, 9}], 1], PrimeQ, 1] == {}]; A032734 = {}; n = 1; While[n < 50000, If[ok[n], Print[n]; AppendTo[A032734, n]]; n++]; A032734(* Jean-François Alcover, Nov 23 2011 *)
Select[Range[50000], NoneTrue[Flatten[Table[FromDigits[Join[{x}, IntegerDigits[ #], {y}]], {x, 9}, {y, 9}]], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 07 2018 *)

Prog

(PARI) is_A032734(n)=p=10^#Str(n*=10); forstep(k=n+p, n+9*p, p, nextprime(k)>k+9 || return); 1 \\ M. F. Hasler, Oct 22 2011
(Python)
from sympy import isprime
def ok(n):
    s, fdigs, edigs = str(n), "123456789", "1379"
    return not any(isprime(int(f+s+e)) for f in fdigs for e in edigs)
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Sep 05 2022

Crossrefs

Cf. A032682, A032683, A032684, A032685.

CF. A032702-A032733.

Sequence in context: A341286 A250710 A278196 * A345518 A345771 A252047

Adjacent sequences: A032731 A032732 A032733 * A032735 A032736 A032737

Keyword

nonn,nice,base

Author

Patrick De Geest, May 15 1998

Status

approved