A090918 Beginning with 3, least prime, greater than the previous term, such that the arithmetic mean of first n terms is a prime.

3, 7, 11, 23, 41, 53, 79, 127, 313, 353, 431, 443, 599, 863, 1049, 1669, 3643, 3919, 4177, 4657, 4861, 5261, 6449, 6737, 7057, 8821, 9013, 9337, 10513, 11161, 13309, 13693, 14449, 14537, 15137, 15377, 15439, 15991, 16231, 16607, 16889, 17489

Offset

1,1

Comments

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

Links

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

Formula

a(n) = n*A090919(n) - (n-1)*A090919(n-1). - Vladimir Shevelev, Nov 24 2012

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]]; Nest[f, {3}, 41] (* 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(A090918[k], ", ") ); A090918}

Crossrefs

Cf. A090940, A090941, A090919.

Sequence in context: A106935 A308576 A116362 * A139253 A283588 A283706

Adjacent sequences: A090915 A090916 A090917 * A090919 A090920 A090921

Keyword

nonn

Author

Amarnath Murthy, Dec 16 2003

Extensions

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

Status

approved