A385280 a(n) is the number of n-digit primes of which all digits except one are the same.
4, 20, 46, 43, 40, 53, 35, 49, 40, 38, 44, 52, 35, 45, 49, 42, 38, 57, 27, 45, 38, 47, 37, 52, 33, 45, 56, 38, 36, 65, 29, 56, 48, 40, 38, 58, 37, 33, 57, 40, 37, 61, 41, 39, 37, 44, 36, 55, 47, 43, 47, 43, 35, 62, 43, 46, 29, 35, 37, 56, 39, 41, 46, 48, 39, 74, 45, 34, 34, 35, 34, 67, 39, 45, 43
Offset: 1
Examples
a(5) = 40 because there are 40 5-digit primes of which all digits but one are the same, namely 10111, 11113, 11117, 11119, 11131, 11161, 11171, 11311, 11411, 16111, 22229, 23333, 31333, 33331, 33343, 33353, 33533, 38333, 44449, 47777, 49999, 59999, 67777, 71777, 76777, 77377, 77477, 77747, 77773, 77797, 77977, 79777, 79999, 88883, 94999, 97777, 98999, 99929, 99989, 99991.
Links
- Robert Israel, Table of n, a(n) for n = 1..1000
Programs
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Maple
f:= proc(n) local i,j,m, m2, t; t:= 0; for i from 1 to 9 do for j in {$0..9} minus {i} do if (n-1)*i + j mod 3 = 0 then next fi; if j = 0 then m2:= n-2 else m2:= n-1 fi; if not member(i,{1,3,7,9}) then m2:= 0 fi; t:= t + nops(select( isprime,{seq((10^n-1)/9*i + 10^m*(j-i),m=0..m2)})) od od; t end proc: f(1):= 4: f(2):= 20: map(f, [$1..100]); -
Python
from gmpy2 import is_prime, digits def a(n): Rn = (10**n-1)//9 return len(set(t for d in range(1, 10) for i in range(n if d in {1, 3, 7, 9} else 1) for c in set(range(-d, 10-d))-{0} if len(digits(t:=d*Rn+c*10**i))==n and is_prime(t))) print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Jun 25 2025
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