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
Examples
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.
Programs
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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
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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
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