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A032734 All 81 combinations of prefixing and following a(n) by a single digit are nonprime. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

2437 prefixed and followed with a pair of digits from (1,2,3,4,5,6,7,8,9) never yields a prime: '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-Fran├žois Alcover, Nov 23 2011 *)

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

CROSSREFS

Cf. A032682-A032685 and A032702-A032733.

Sequence in context: A192767 A250710 A278196 * A252047 A083625 A253842

Adjacent sequences:  A032731 A032732 A032733 * A032735 A032736 A032737

KEYWORD

nonn,nice,base,changed

AUTHOR

Patrick De Geest, May 15 1998

STATUS

approved

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Last modified June 22 23:15 EDT 2017. Contains 288633 sequences.