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

1,1

Links

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A064336.

Sequence in context: A156611 A143509 A111166 * A076873 A089440 A354789

Adjacent sequences: A064334 A064335 A064336 * A064338 A064339 A064340

Keyword

easy,nonn,changed

Author

Lior Manor, Sep 13 2001

Status

approved