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

1,1

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

Links

Table of n, a(n) for n=1..4.

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A133584.

Sequence in context: A201092 A264363 A232313 * A189277 A012170 A264269

Adjacent sequences: A133580 A133581 A133582 * A133584 A133585 A133586

Keyword

more,nonn,base

Author

Enoch Haga, Sep 17 2007, Sep 18 2007

Status

approved