

A073684


Sum of next a(n) successive primes is prime.


10



2, 3, 5, 3, 5, 3, 3, 7, 9, 5, 9, 7, 3, 7, 5, 3, 3, 3, 5, 3, 3, 3, 5, 5, 57, 25, 49, 3, 9, 5, 11, 3, 5, 5, 5, 5, 17, 25, 3, 3, 5, 3, 7, 9, 5, 3, 3, 3, 15, 3, 3, 3, 3, 3, 3, 3, 15, 3, 5, 33, 5, 3, 3, 9, 7, 3, 33, 3, 3, 5, 3, 15, 3, 5, 9, 7, 13, 5, 11, 3, 3, 11
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OFFSET

1,1


COMMENTS

Group the primes such that the sum of each group is a prime. Each group from the second onwards should contain at least 3 primes: (2, 3), (5, 7, 11), (13, 17, 19, 23, 29), (31, 37, 41), (43, 47, 53, 59, 61), ... Sequence gives number of terms in each group.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1)=2 because sum of first two primes 2+3 is prime; a(2)=3 because sum of next three primes 5+7+11 is prime; a(3)=5 because sum of next five primes 13+17+19+23+29 is prime.


MATHEMATICA

f[l_List] := Block[{n = Length[Flatten[l]], k = 3, r}, While[r = Table[Prime[i], {i, n + 1, n + k}]; ! PrimeQ[Plus @@r], k += 2]; Append[l, r]]; Length /@ Nest[f, {{2, 3}}, 100] (* Ray Chandler, May 11 2007 *)
cnt = 0; Table[s = Prime[cnt+1] + Prime[cnt+2]; len = 2; While[! PrimeQ[s], len++; s = s + Prime[cnt+len]]; cnt = cnt + len; len, {n, 100}] (* T. D. Noe, Feb 06 2012 *)


CROSSREFS

Cf. A073682(n) is the sum of terms in nth group, A073683(n) is the first term in nth group, A077279(n) is the last term in nth group.
Sequence in context: A001269 A201769 A077276 * A179295 A083776 A122820
Adjacent sequences: A073681 A073682 A073683 * A073685 A073686 A073687


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Aug 11 2002


EXTENSIONS

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 10 2003
Extended by Ray Chandler, May 02 2007


STATUS

approved



