A173448 Smallest prime(k) such that the concatenation prime(k)//prime(k+1)//...//prime(k+n-1) represents an emirp.

13, 151, 353, 139, 101, 70451, 97, 15193, 3821, 9319, 7717, 103619, 10883, 18353, 108821, 701, 10091, 99251, 78497, 3559, 930043, 99787, 18671, 12251, 711751, 9293, 10861, 121921, 103099, 986189, 74287, 796567, 323003, 108707, 365779, 192377, 393901, 380251, 98479, 114343, 329729

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..125

Example

a(5) = 101 because 101103107109113 = A086041(6) is the smallest emirp formed by concatenating 5 consecutive primes (101, 103, 107, 109, 113).

Maple

f:= proc(n) local L, p, a, i, d, flag, x, y;
      L:= [seq(ithprime(i), i=1..n)];
      do
        d:= ilog10(L[2]);
        a:= floor(L[2]/10^d);
        flag:= true;
        if member(a, {2, 6, 8}) then p:= nextprime((a+1)*10^d)
        elif member(a, {4, 5}) then p:= nextprime(7*10^d)
        else flag:= false
        fi;
        if flag then
           L:= p; for i from 1 to n-1 do p:= nextprime(p); L:= L, p od;
           L:= [L]
        else
          L:= [op(L[2..-1]), nextprime(L[-1])]
        fi;
        x:= lcat(L);
        if isprime(x) then
          y:= rev(x);
          if isprime(y) and y <> x then return L[1] fi;
        fi
     od
end proc:
f(1):= 13:
map(f, [$1..50]); # Robert Israel, May 19 2026

Crossrefs

Cf. A006567, A167518, A030996.

Sequence in context: A051475 A382898 A242576 * A386359 A396245 A097168

Adjacent sequences: A173445 A173446 A173447 * A173449 A173450 A173451

Keyword

nonn,base

Author

Lekraj Beedassy, Feb 18 2010

Extensions

Keyword:base added and definition reworded by R. J. Mathar, Feb 24 2010

More terms from Sean A. Irvine, Nov 14 2010

Status

approved