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A123994 Smallest number k such that prime(n)^k is a sum of 3 consecutive primes. 1
64, 57, 2, 2, 107, 203, 1133, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
a(13) through a(23): { 1, 2, 3, 8, 1, 4, 6, 1, 729, 5, 1 }.
a(12) > 5387. a(24) > 3320.
Smallest prime p such that p^n is equal to the sum of 3 consecutive primes is given by A122706(n).
LINKS
EXAMPLE
a(1) does not exist because there is no power of 2 that is a sum of 3 consecutive primes.
prime(5)^2 = 11^2 = 121 can be written as 37+41+43, therefore a(5)=2.
PROG
(PARI) { A123994(n) = my(k, t1, t2, t3, m); k=0; while(1, k++; m=prime(n)^k; t1=precprime(m/3); t2=nextprime(m/3); t3=m-t1-t2; if( ispseudoprime(t3) && ( (t3<t1 && t3==precprime(t1-1)) || (t3>t2 && t3==nextprime(t2+1)) ), return(k)); ); }
CROSSREFS
Cf. A122706.
Sequence in context: A252486 A188828 A331224 * A248770 A272297 A291094
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Oct 31 2006, Nov 02 2006
EXTENSIONS
Corrected by R. J. Mathar, Jan 13 2007
a(8)-a(11) from Max Alekseyev, Apr 24 2010
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)