A172514 First prime not the middle of a prime two digits longer in base n.

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

Links

Table of n, a(n) for n=2..28.

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).

Cf. A247593, A247699.

Sequence in context: A243583 A215487 A146037 * A128024 A245723 A118128

Adjacent sequences: A172511 A172512 A172513 * A172515 A172516 A172517

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