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A172514
First prime not the middle of a prime two digits longer in base n.
2
3, 7, 19, 97, 823, 3499, 2777, 6827, 2437, 21523, 300299, 446273, 339769, 1168523, 14117417, 29227421, 14160061, 78521987, 161187707, 1200085823, 2125209127, 1369430897, 56378083771, 26054006611, 76375900241, 290373503549, 640442460709
OFFSET
2,1
EXAMPLE
In base n=10, 2437 is the least prime such that all numbers of the form x2437y where x and y are digits [1..9] are composite, so a(10)=2437.
PROG
(PARI) isok(p, n) = my(m=logint(p, n)+1); for (x=1, n-1, my(q = x*n^m+p); for (y=1, n-1, if (isprime(n*q+y), return (0)); ); ); return(1);
a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p; \\ Michel Marcus, Sep 04 2022
(Python)
from sympy import isprime, nextprime
def digits(n, b):
c = 0
while n >= b: n //= b; c += 1
return c + 1
def a(n):
p = 2
while True:
d, p1, found = digits(p, n), n*p, True
for f in range(n**(d+1), n**(d+2), n**(d+1)):
for e in range(0, n, 2) if (f+p1)%2 else range(1, n, 2):
if isprime(f + p1 + e): found = False; break
if not found: break
if found: return p
p = nextprime(p)
print([a(n) for n in range(2, 15)]) # Michael S. Branicky, Sep 05 2022
CROSSREFS
Cf. A032734 (in base 10 and not limited to primes).
Sequence in context: A243583 A215487 A146037 * A128024 A245723 A118128
KEYWORD
nonn,base,more
AUTHOR
James G. Merickel, Feb 05 2010
EXTENSIONS
a(24)-a(26) added by James G. Merickel, Sep 22 2014
a(26) removed (see user talk page) by Bill McEachen, Sep 03 2022
a(26) from Michael S. Branicky, Sep 20 2022
a(27) from Michael S. Branicky, Jul 10 2023
a(28) from Michael S. Branicky, Jul 12 2023
STATUS
approved