A090919 Primes arising as the arithmetic mean of first n terms of A090918.

3, 5, 7, 11, 17, 23, 31, 43, 73, 101, 131, 157, 191, 239, 293, 379, 571, 757, 937, 1123, 1301, 1481, 1697, 1907, 2113, 2371, 2617, 2857, 3121, 3389, 3709, 4021, 4337, 4637, 4937, 5227, 5503, 5779, 6047, 6311, 6569, 6829, 7079, 7349, 7639, 7927, 8263, 8599

Offset

1,1

Comments

a(1000) = 13918649. - Rick L. Shepherd, Mar 08 2004

Intersection of A090918 and A090919: 3,7,11,23,11161,4197541. - Zak Seidov, Apr 05 2011.

Contribution by Vladimir Shevelev, Nov 24 2012 (Start)

A recursive algorithm of parallel calculation of A090918 and A090919.

Together with a(n)=A090919(n), denote b(n)=A090918(n). We begin with a(1)=b(1)=3; if, for n>=2, we know a(n-1) and b(n-1), then a(n) is the smallest prime x such that n*x-(n-1)*a(n-1) is a prime greater than b(n-1). Now, knowing a(n), we have b(n) = n*a(n) - (n-1)*a(n-1).

For example, suppose that we know that a(5)=17, b(5)=41. To find a(6) and b(6), consider inequality 6*x - 5*17 > 41, where x is prime. Thus we consider x >= 23. Since, already for x=23, 6*x-5*17=53 is prime, then a(6)=23, b(6)=53. (End)

Links

Zak Seidov, Table n, a(n) for n=1..2000

Mathematica

f[s_] := Block[{m = 1 + Length@ s, p = NextPrime@ s[[-1]], ss = Plus @@ s}, While[ !PrimeQ[(ss + p)/m], p = NextPrime@ p]; Append[s, p]]; s = Nest[f, {3}, 41]; (Accumulate@ s)/Range@ 42 (* Robert G. Wilson v, Dec 15 2012 *)

Prog

(PARI) {terms=100; A090918=A090919=vector(terms); A090918[1]=A090919[1]=3; s=0; for(k=2, terms, s=s+A090918[k-1]; p=A090918[k-1]+1; until(isprime(p) && (denominator((s+p)/k)==1) && isprime((s+p)/k), p++); A090918[k]=p; A090919[k]=(s+p)/k; print1(A090919[k], ", ") ); A090919}

Crossrefs

Cf. A090940, A090941, A090918.

Sequence in context: A170886 A361823 A238137 * A065557 A266164 A152999

Adjacent sequences: A090916 A090917 A090918 * A090920 A090921 A090922

Keyword

nonn

Author

Amarnath Murthy, Dec 16 2003

Extensions

Corrected and extended by Rick L. Shepherd, Mar 08 2004

Status

approved