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Search: id:A112418
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| A112418 |
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Primes which have a prime number of partitions into five distinct primes. |
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+0
1
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| 53, 59, 67, 83, 113, 151, 157, 211, 239, 601, 809, 821, 881, 971, 1237, 1297, 1427, 1669, 1759, 1973, 2069, 2129, 2243, 2333, 2659, 2677, 2719, 2789, 2803, 2999
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The corresponding numbers of partitions are 2,5,11,29,109,331,379,1091...
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EXAMPLE
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53 is there because there are 2 partitions of 53 (3+7+11+13+19, 5+7+11+13+17) and 2 is prime.
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MAPLE
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part5_prime:=proc(N) s:=1; for n from 2 to N do cont:=0; for i from 1 to n-5 do for j from i+1 to n-4 do for k from j+1 to n-3 do for l from k+1 to n-2 do for m from l+1 to n-1 do if(ithprime(n)= ithprime(i)+ithprime(j)+ithprime(k)+ithprime(l)+ithprime(m) then cont:=cont+1; fi; od; od; od; od; od; if (isprime(cont)=true) then a[s]:=ithprime(n); s:=s+1; fi; od; end:
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CROSSREFS
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Cf. A000009, A000041, A007963, A051034.
Sequence in context: A095529 A095519 A095509 this_sequence A059497 A059472 A079593
Adjacent sequences: A112415 A112416 A112417 this_sequence A112419 A112420 A112421
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KEYWORD
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nonn
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AUTHOR
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Giorgio Balzarotti and Paolo P. Lava (greenblue(AT)tiscali.it), Dec 09 2005
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Jan 26 2006
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