A133583 Index of smallest prime number where n consecutive leading digits of the index match n consecutive leading digits in the prime.

169, 5591, 6438, 6455

Offset: 1

Author

Enoch Haga, Sep 17 2007, Sep 18 2007

Keywords

• more
• nonn
• base

Comments

Puzzle 217 on Carlos Rivera's The Prime Puzzles & Problems Connection has anticipated some of the concepts of this sequence. Several people have contributed to this puzzle and some of its terms may be seen there. In particular, the first page of the puzzle includes a term in this sequence.

72258*10^37 < a(5) < 74142*10^37. - Max Alekseyev, Sep 29 2015

Examples

			a(2)=5591 because this is the index of prime 55001 where n=2 and 55 in the index matches the first two leading digits of the prime.
		

Links

• Carlos Rivera's The Prime Puzzles & Problems Connection, Puzzle 217

Crossrefs

Cf. A133584.

Programs

Maple

A133583 := proc(n)
    local p,i,dgsi,dgsp,d,wrks;
    p := 2 ;
    for i from 1 do
        dgsi := convert(i,base,10) ;
        dgsp := convert(p,base,10) ;
        if nops(dgsi) >= n and nops(dgsp) >= n then
            wrks := true;
            for d from 1 to n do
                if op(-d,dgsi) <> op(-d,dgsp) then
                    wrks := false ;
                    break;
                end if;
            end do:
            if wrks then
                return i;
            end if;
        end if;
        p := nextprime(p) ;
    end do:
end proc: # R. J. Mathar, Feb 14 2015

Mathematica

Table[ind = 10^(n - 1); While[Take[IntegerDigits[ind], n] !=
Take[IntegerDigits[Prime[ind]], n], ind++]; ind, {n, 1, 4}] (* Robert Price, Apr 11 2019 *)

Formula

a(n) = A000720(A133584(n))