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URL: https://oeis.org/A229206

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A229206
n-th prime that begins with prime(n).
1
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
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: A129900 A262834 A376205 * A105757 A091252 A031920
KEYWORD
base,nonn
AUTHOR
Michel Marcus, Sep 16 2013
STATUS
approved