A064336 Maximal prime numbers with increasing prime differences.

2, 3, 5, 7, 13, 23, 31, 47, 61, 83, 109, 139, 173, 211, 251, 293, 337, 389, 449, 509, 577, 647, 719, 797, 883, 977, 1069, 1171, 1277, 1381, 1493, 1619, 1747, 1879, 2017, 2161, 2311, 2467, 2621, 2777, 2939, 3109, 3271, 3461, 3643, 3833, 4027, 4231, 4451, 4673

Offset: 1

Author

Lior Manor, Sep 13 2001

Keywords

• easy
• nonn

Examples

			a(5) = 13, since a(4) = 7, p(4) = 7 and 13 is the largest prime which is not larger than 7 + 7.
		

Links

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

Crossrefs

Cf. A064337.

Programs

Mathematica

PrevPrime[n_] := (k = n; While[ ! PrimeQ[k], k-- ]; k); f[1] = 2; f[n_] := PrevPrime[ f[n - 1] + Prime[n] ]; Table[ f[n], {n, 1, 50} ]

PARI

{ for (n=1, 1000, if (n>1, a=precprime(a + prime(n - 1)), a=2); write("b064336.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 12 2009

Formula

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