A070865 Smallest prime such that the difference of successive terms is strictly increasing.

2, 3, 5, 11, 19, 29, 41, 59, 79, 101, 127, 157, 191, 227, 269, 313, 359, 409, 461, 521, 587, 659, 733, 809, 887, 967, 1049, 1151, 1259, 1373, 1489, 1607, 1733, 1861, 1993, 2129, 2267, 2411, 2557, 2707, 2861, 3019, 3181, 3347, 3517, 3691, 3877, 4073, 4271

Offset: 1

Author

Amarnath Murthy, May 16 2002

Keywords

• nonn

Comments

The slowest increasing sequence of primes with strictly increasing difference of successive terms. - Zak Seidov and Charles R Greathouse IV, May 01 2015

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070866.

Programs

Mathematica

d=0; p=2; t={p}; Do[d=NextPrime[p+d]-p; AppendTo[t,p+=d], {99}]; t (* Vladimir Joseph Stephan Orlovsky, May 29 2010 *)
nxt[{a_,b_}]:={b,NextPrime[2b-a]}; Transpose[NestList[nxt,{2,3},50]][[1]] (* Harvey P. Dale, Jan 04 2015 *)

PARI

t=0; print1(last=2); while(1, n=last+t; while(!isprime(n++), ); print1(", "n); t=n-last; last=n) \\ Charles R Greathouse IV, Apr 30 2015

Formula

a(n) >> n^2. - Charles R Greathouse IV, Apr 30 2015

Extensions

Corrected and extended by Lior Manor, Jun 02 2002