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 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 (list; graph; refs; listen; history; text; internal format)
 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 n-th group, A073683(n) is the first term in n-th group, A077279(n) is the last term in n-th 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

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Last modified February 28 20:40 EST 2024. Contains 370400 sequences. (Running on oeis4.)