A216418 Fortunate numbers with increasing multiplicity.

3, 23, 61, 331, 2837, 18169

Offset: 1

Author

Charles R Greathouse IV, Sep 06 2012

Keywords

• nonn
• hard
• more

Comments

a(n) appears in A005235 more often than any preceding term.

Is this sequence infinite?

Examples

			3 is the first term of A005235, so a(1) = 3. A005235(5) = A005235(8) = 23, while smaller primes appear only once, so a(2) = 23.
		

Crossrefs

Cf. A005235, A046066.

Programs

PARI

ct(p)=my(pr=1,s);forprime(q=2,p-1,if(!ispseudoprime((pr*=q)+p), next);forprime(r=q+1,p-1,if(ispseudoprime(pr+r),next(2)));s++);s
r=0;forprime(p=2,2e3,t=ct(p);if(t>r,r=t;print1(p", ")))

Extensions

a(6) from Charles R Greathouse IV, Sep 17 2012