A226935 Least prime p(1) beginning a chain of primes p(i) = i*p(i-1) - (i-1) for i = 2, 3, ..., n.

2, 2, 2, 19, 19, 8629, 748669, 2506981, 228698251, 228698251

Offset: 1

Author

Robin Garcia, Jun 22 2013

Keywords

• nonn
• more

Comments

Initial primes p(1) cannot be 3 mod 10 (except p(1) = 3) because p(2) would be 5 mod 10, not prime, and cannot be 7 mod 10 because p(4) would be 5 mod 10, not prime.

Examples

			a(5) --> p(1) = 19 because p(2) = 2*p(1) - 1 = 37, p(3) = 3*p(2) - 2 = 109, p(4) = 4*p(3) - 3 = 433, p(5) =5*p(4) - 4 = 2161 are primes.
		

Crossrefs

Cf. A005603, A088251.

Programs

PARI

\\ Find a(9)
n=8; v=vector(n); forprime(p=2,10^9,i=0; a=2*p-1; b=3*a-2; c=4*b-3; d=5*c-4; e=6*d-5; f=7*e-6; g=8*f-7; h=9*g-8; if(isprime(a),i++; v[1]=a, v[1]=0); if(isprime(b), i++; v[2]=b, v[2]=0); if(isprime(c), i++; v[3]=c, v[3]=0); if(isprime(d), i++; v[4]=d, v[4]=0); if(isprime(e), i++; v[5]=e, v[5]=0); if(isprime(f), i++; v[6]=f, v[6]=0); if(isprime(g), i++; v[7]=g, v[7]=0); if(isprime(h), i++; v[8]=h, v[8]=0); if(i>n-1,print([p,v, i])))

PARI

ct(p); my(i=2); while(isprime(p=i*p-i+1), i++); i
a(n)=forprime(p=2,, if(ct(p)>n, return(p))) \\ Charles R Greathouse IV, Sep 27 2015

Formula

p(i) - p(i-1) = (i! - (i-1)!)*(p(1) - 1).