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A071234 Smallest prime beginning and ending in 2n+1 or 0 if no such prime exists. 2
11, 3, 5, 7, 919, 11, 13, 0, 17, 19, 21121, 23, 0, 27127, 29, 31, 33533, 0, 37, 39139, 41, 43, 0, 47, 49549, 51151, 53, 0, 57457, 59, 61, 63463, 0, 67, 690269, 71, 73, 0, 77377, 79, 81181, 83, 0, 87187, 89, 91291, 93493, 0, 97 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

If the two copies of the 2n+1 are not allowed to share digits, a(1) is not 3, a(2) is not 5 and a(3) is not 7 and a(5) is not 11, which results in A070278.

Conjecture: a(n) = 0 if and only if n > 2 and n == 2 mod 5 (which makes 2*n+1 == 0 mod 5). - Robert Israel, May 26 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

EXAMPLE

a(6060) = 1212121, because it is the smallest prime beginning and ending in 2*6060+1 = 12121.

a(7+5*k) = 0, because 2*(7+5*k)+1 = 15+10*k == 0 (mod 5) is no prime.

MAPLE

A071234 := proc(n)

        local dgsn , p, wrks, doff;

        dgsn := convert(2*n+1, base, 10) ;

        for i from 1 to 1000000 do

                p := ithprime(i) ;

                wrks := true;

                dgsp := convert(p, base, 10) ;

                doff := nops(dgsp)-nops(dgsn) ;

                if doff >= 0 then

                        for d from 1 to nops(dgsn) do

                                if op(d, dgsp) <> op(d, dgsn) then

                                        wrks := false;

                                        break;

                                end if;

                                if op(d+doff, dgsp) <> op(d, dgsn) then

                                        wrks := false;

                                        break;

                                end if;

                        end do:

                        if wrks then

                                return p

                        end if;

                end if;

        end do:

        return 0 ;

end proc: # R. J. Mathar, Feb 03 2011

# Alternative:

f:= proc(n)

    local u, d, r, x, y;

    u:= 2*n+1;

    if isprime(u) then return(u) fi;

    if u mod 5 = 0 then return(0) fi;

    d:= ilog10(u);

    for r from 0 do

      for x from 0 to 10^(r+1)-1 do

       y:= u + 10^(d+1)*x + 10^(r+d+2)*u;

      if isprime(y) then return(y) fi

    od od

end proc:

11, seq(f(n), n=1..100); # Robert Israel, May 26 2015

PROG

(Sage)

def A071234(n):

    s = str(2*n+1)

    if s.endswith('5') and not s == '5': return 0

    for p in Primes():

        ps = str(p)

        if ps.startswith(s) and ps.endswith(s): return p

[A071234(n) for n in range(20)]

# D. S. McNeil, Feb 03 2011

CROSSREFS

Cf. A070278.

Sequence in context: A070720 A010189 A338716 * A082626 A334132 A245193

Adjacent sequences:  A071231 A071232 A071233 * A071235 A071236 A071237

KEYWORD

nonn,base

AUTHOR

Amarnath Murthy, May 18 2002

STATUS

approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)