A229206 n-th prime that begins with prime(n).

2, 31, 59, 79, 1117, 1303, 1733, 1913, 2347, 2963, 3169, 3769, 41017, 43003, 47017, 53069, 59053, 61027, 67043, 71119, 73079, 79147, 83117, 89113, 97151, 101117, 103099, 107197, 109159, 113147, 127247, 131231, 137251, 139303, 149239, 151247, 157219, 163337

Offset

1,1

Comments

Diagonal of triangle A114009.

Links

Robert Israel, Table of n, a(n) for n = 1..4000

Maple

f:= proc(n) local p, q, d, count, i;
  p:= ithprime(n); count:= 1;
  for d from 1 do
    q:= 10^d*p;
    for i from count do
      q:= nextprime(q);
      if q > 10^d*(p+1) then break fi;
      count:= count+1;
      if count = n then return q fi;
  od od;
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Jan 19 2023

Prog

(PARI) ok(np, dfp) = {dnp = digits(np); xdnp = vector(#dfp, id, dnp[id]); xdnp == dfp; }
findnextp(p, dfp) = {np = nextprime(p+1); while (! ok(np, dfp), np = nextprime(np+1)); np; }
a(n) = {p = fp = prime(n); dfp = digits(fp); for (k = 2, n, p = findnextp(p, dfp); ); p; } \\ Michel Marcus, Sep 16 2013
(Python)
from itertools import count
from sympy import isprime, prime
def a(n):
    if n == 1: return 2
    pn, c = prime(n), 1
    for d in count(1):
        pow10 = 10**d
        base = pn * pow10
        for i in range(1, pow10, 2):
            t = base + i
            if isprime(t): c += 1
            if c == n: return t
print([a(n) for n in range(1, 41)]) # Michael S. Branicky, Jan 19 2023

Crossrefs

Cf. A114009.

Sequence in context: A370157 A129900 A262834 * A105757 A091252 A031920

Adjacent sequences: A229203 A229204 A229205 * A229207 A229208 A229209

Keyword

base,nonn

Author

Michel Marcus, Sep 16 2013

Status

approved