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Search: id:A127313
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| A127313 |
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Primes p such that p+q+r, where p, q, r are consecutive primes, equals s+t+1, where s and t are consecutive primes. |
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3
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| 7, 37, 53, 59, 61, 67, 71, 83, 97, 149, 173, 181, 233, 271, 277, 283, 307, 421, 521, 541, 569, 613, 617, 673, 691, 719, 809, 859, 877, 971, 983, 1031, 1039, 1181, 1237, 1297, 1319, 1381, 1423, 1453, 1459, 1471, 1483, 1543, 1579, 1607, 1609, 1787, 1861, 1931
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The smallest of three consecutive primes whose sum is equal to 1 plus the sum of two consecutive primes.
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EXAMPLE
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37, 41, 43 are consecutive primes, 37+41+43 =121; 59 and 61 are consecutive primes, 59+61+1 = 121. Hence 37 is a term.
19, 23, 29 are consecutive primes, 19+23+29 = 71; 31 and 37 are consecutive primes, 31+37+1 = 69 < 71; 37 and 41 are the next pair of consecutive primes, 37+41+1 = 79 > 71. Hence there are no consecutive primes s and t with s+t+1 = 71 and 19 is not in the sequence.
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MAPLE
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B:={seq(1+ithprime(k)+ithprime(k+1), k=1..500)}: a:=proc(n) if member(ithprime(n)+ithprime(n+1)+ithprime(n+2), B)=true then ithprime(n) else fi end: seq(a(n), n=1..900); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2007
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PROGRAM
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(MAGMA) [ p: p in PrimesInInterval(3, 1950) | not IsPrime(k) and PreviousPrime(k)+NextPrime(k) eq 2*k where k is (p+NextPrime(p)+NextPrime(NextPrime(p))-1) div 2 ]; /* Klaus Brockhaus, Apr 03 2007 */
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CROSSREFS
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Sequence in context: A106924 A076285 A077720 this_sequence A003521 A078626 A093342
Adjacent sequences: A127310 A127311 A127312 this_sequence A127314 A127315 A127316
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Mar 28 2007
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EXTENSIONS
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Edited, corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 01 2007
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