A084106 Larger difference (r-q or q-p) associated with A084105.

2, 6, 14, 10, 12, 18, 22, 24, 28, 30, 34, 42, 52, 54, 58, 60, 70, 82, 90, 100, 118, 132, 136, 148, 150, 168, 178, 196, 208, 214, 220, 234, 250, 288, 310, 318, 330, 360, 366, 384, 390, 402, 408, 414, 454, 462, 516, 588, 598, 610, 648, 706, 712, 736, 754, 756, 760

Offset: 1

Author

Hugo Pfoertner, May 29 2003

Keywords

• nonn

Comments

Differences > a(46) = 462 require search beyond 10^12. - Hugo Pfoertner, Sep 02 2020

Searched range through 10^13. - Hugo Pfoertner, Sep 17 2020

Examples

			a(5)=12 because the larger difference between A084105(5)=199 and its prime neighbors 197 and 211 is 211-199=12.
a(51)=648 corresponds to the gaps between the 3 consecutive primes 9787731507761, 9787731508409, 9787731508411. - _Hugo Pfoertner_, Sep 19 2020
		

Crossrefs

Cf. A002386, A084105, A337489.

Programs

PARI

default(realprecision,20); default(primelimit,436270000); { apt(m)= local(dl,dr,q,qm); qm=1.0; for(n=2,m, dl=prime(n)-prime(n-1); dr=prime(n+1)-prime(n); q=min(dl,dr)/max(dl,dr)+0.; if(q
				

PARI

a084106(limit)={my(p1=2,p2=3,q=0);forprime(k=5,limit,my(r=max((p2-p1)/(k-p2),(k-p2)/(p2-p1)));if(r>q,q=r;print1(max(p2-p1,k-p2),", "));p1=p2;p2=k)};
a084106(10^9) \\ Hugo Pfoertner, Sep 02 2020

Extensions

More terms from Don Reble and Jason Earls, May 29 2003

a(36)-a(46) from Hugo Pfoertner, Sep 02 2020

a(47)-a(51) from Hugo Pfoertner, Sep 17 2020

a(52)-a(57) from Martin Ehrenstein, Aug 07 2021