A064337 Minimal prime numbers with increasing prime differences.

2, 5, 11, 17, 29, 41, 59, 79, 101, 127, 157, 191, 229, 271, 317, 367, 421, 487, 557, 631, 709, 787, 877, 967, 1061, 1163, 1277, 1381, 1489, 1601, 1721, 1861, 1993, 2131, 2273, 2423, 2579, 2741, 2909, 3079, 3253, 3433, 3617, 3821, 4019, 4217, 4421, 4637

Offset: 1

Author

Lior Manor, Sep 13 2001

Keywords

• easy
• nonn

Examples

			a(5) = 29, since a(4) = 17, p(4) = 7 and 29 is the smallest prime which is not smaller than 17 + 7.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A064336.

Programs

Mathematica

NextPrime[n_] := (k = n; While[ ! PrimeQ[k], k++ ]; k); f[1] = 2; f[n_] := NextPrime[ f[n - 1] + Prime[n-1] ]; Table[ f[n], {n, 1, 50} ]
Transpose[NestList[{First[#]+1,NextPrime[Last[#]+Prime[First[#]]]}&, {1,2}, 50]][[2]] (* Harvey P. Dale, Oct 23 2011 *)

PARI

for (n=1, 1000, if (n>1, a=nextprime(a + prime(n - 1)), a=2); write("b064337.txt", n, " ", a) )  \\ Harry J. Smith, Sep 12 2009

Formula

a(1) = 2, a(n+1) = MIN {prime p | p >= a(n) + prime(n)} (where prime(n) is the n-th prime number).

Conjecture: a(n) ~ K*n^2*log(n). - Bill McEachen, Apr 04 2024

a(n) >= A007504(n) >> n^2 log n. On Cramér's conjecture, a(n) << n^2 log^2 n. - Charles R Greathouse IV, Apr 10 2024