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A064337
Minimal prime numbers with increasing prime differences.
3
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
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
KEYWORD
easy,nonn
AUTHOR
Lior Manor, Sep 13 2001
STATUS
approved