A276988 a(n) is the least k such that 10*k+prime(n) is composite.

1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1

Offset: 1

Author

Yves Debeuret, Sep 24 2016

Keywords

• nonn

Comments

It appears that a(n)<3 for n>2 (checked up to 10^7).

This comment is surely true since every prime except 3 equals 1 or 2 mod 3, so the addition of 10 == 1 mod 3 once or twice makes it divisible by 3. So (3 - (prime(n) mod 3)) is an upper bound. - Andrey Zabolotskiy, Nov 01 2016

Examples

			For n=1, 10+2=3x4 so a(1)=1;
For n=2, 13 and 23 are prime, but then 30+3=3x11 so a(2)=3;
For n=3, 10+5=3x5 so a(3)=1;
For n=4, 17 is prime, but then 20+7=3x9 so a(4)=2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

f:= proc(n) local p,k;
  p:= ithprime(n);
  for k from 1 do if not isprime(p+10*k) then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 04 2024

PARI

isc(n) = (n > 1) && !isprime(n);
a(n) = my(k = 0, p = prime(n)); while(!isc(p+10*k), k++); k; \\ Michel Marcus, Sep 27 2016

Extensions

More terms from Michel Marcus, Sep 27 2016