A090497 Smallest prime p such that the concatenation 2,3,5,7, ... (primes) ... p is a multiple of prime(n).

2, 29, 5, 11, 17, 61, 31, 271, 3, 13, 107, 1051, 439, 211, 5, 1153, 149, 23, 37, 173, 593, 173, 281, 347, 191, 433, 2083, 109, 389, 1453, 277, 383, 227, 443, 1879, 11, 233, 353, 191, 1723, 547, 241, 397, 181, 199, 7549, 79, 11, 547, 877, 313, 1213, 409, 79, 2969

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(4) = 11 and 235711 is a multiple of prime(4) = 7.

Maple

N:= 100: # for a(1)..a(N)
P:= [seq(ithprime(i), i=1..N)]:
R:= Vector(N): count:= 0:
p:= 1: s:= 0:
while count < N  do
  p:= nextprime(p);
  s:= 10^(1+ilog10(p))*s+p;
  r:= select(t -> R[t]=0 and s mod P[t] = 0, [$1..N]);
  R[r]:= p;
  count:= count+nops(r);
od:
convert(R, list); # Robert Israel, Oct 28 2021

Mathematica

f[n_] := Block[{p = Prime[n], k = 1, q = 2}, While[ Mod[q, p] != 0, k++; q = FromDigits[ Join[ IntegerDigits[q], IntegerDigits[ Prime[k]]]]]; Prime[k]]; Table[ f[n], {n, 1, 55}]

Prog

(Python)
from sympy import prime, nextprime
def a(n):
    pstr, pn, p = "2", prime(n), 2
    while int(pstr)%pn != 0:
        p = nextprime(p)
        pstr += str(p)
    return p
print([a(n) for n in range(1, 56)]) # Michael S. Branicky, Oct 28 2021

Crossrefs

Sequence in context: A080266 A308757 A180423 * A128371 A175932 A370322

Adjacent sequences: A090494 A090495 A090496 * A090498 A090499 A090500

Keyword

nonn,base

Author

Amarnath Murthy, Dec 03 2003

Extensions

Corrected and extended by Robert G. Wilson v, Dec 05 2003

Status

approved