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A067191 Numbers that can be expressed as the sum of two primes in exactly five ways. 12
48, 54, 64, 70, 74, 76, 82, 86, 94, 104, 124, 136, 148, 158, 164, 188 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There are no other terms below 10000 and I conjecture there are no further terms in this sequence and A067188, A067189, etc. - Peter Bertok (peter(AT)bertok.com), Jan 13 2002
I believe that these conjectures follow from a more general one by Hardy and Littlewood (probably in Some problems of 'partitio numerorum' III, on the expression of a number as a sum of primes, Acta Math. 44(1922) 1-70). - R. K. Guy, Jan 14 2002
There are no further terms through 50000. - David Wasserman, Jan 15 2002
LINKS
EXAMPLE
70 is a term as 70 = 67 + 3 = 59 + 11 = 53 + 17 = 47 + 23 41 + 29 are all the five ways to express 70 as a sum of two primes.
MATHEMATICA
upperbound=10^4; range=ConstantArray[0, 2*upperbound];
primeRange=Prime[Range[PrimePi[upperbound]]];
(range[[Plus@@#]]++)&/@(DeleteDuplicates[Sort[#]&/@Tuples[primeRange, 2]]); {"upperbound="<>ToString[upperbound], Flatten[Position[Take[range, upperbound], 5]]} (* Hans Rudolf Widmer, Jul 06 2021 *)
CROSSREFS
Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), A067187 (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), this sequence (k=5), A066722 (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).
Sequence in context: A357429 A258694 A328738 * A080854 A255267 A366250
KEYWORD
nonn,fini,full
AUTHOR
Amarnath Murthy, Jan 10 2002
EXTENSIONS
Corrected and extended by Peter Bertok (peter(AT)bertok.com), Jan 13 2002
STATUS
approved

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Last modified June 19 15:41 EDT 2024. Contains 373503 sequences. (Running on oeis4.)