A372238 Least number m such that 9*k*m+1 is prime for k=1..n.

2, 2, 4, 170, 9860, 23450, 56980, 56980, 6723767050, 48276858630, 77460393371130, 97581361797920, 97581361797920, 1269928100726715430

Offset: 1

Author

Jean-Marc Rebert, Apr 23 2024

Keywords

• nonn
• hard
• more

Examples

			a(1) = 2, because 9*1*2 + 1 = 19 is prime and no lesser number has this property.
		

Links

• David A. Corneth, PARI program

Crossrefs

Cf. A372188, A088250.

Programs

Mathematica

p[m_, n_] := AllTrue[Range[n], PrimeQ[9*#*m + 1] &];
a[n_] := a[n] = Module[{m = 1}, While[! p[m, n], m++]; m]
Table[a[n], {n, 1, 9}] (* Robert P. P. McKone, May 02 2024 *)

PARI

is(n,m)=my(u=vector(n,k,9*k*m+1));for(i=1,n,if(!isprime(u[i]),return(0)));1
a(n)=my(pas=1);if(n<15,if(n>2,pas=factorback(primes(primepi(n)));pas/=3;my(m=pas));forstep(m=pas,+oo,pas,if(is(n,m),return(m))))

PARI

See PARI link

Formula

If A088250(n) is divisible by 9, then a(n) = A088250(n) / 9. - Jason Yuen, Apr 25 2024

Extensions

a(11)-a(13) from David A. Corneth, Apr 24 2024

a(14) from Jason Yuen, Apr 25 2024