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Search: id:A096134
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| A096134 |
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a(1) = 2; for n > 1: a(n) = least multiple m of n such that m is coprime to n+1 and the absolute difference of a(n) and a(n-1) is a prime distinct from all earlier such differences of consecutive terms. |
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3
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| 2, 4, 9, 12, 5, 18, 7, 80, 9, 40, 11, 48, 65, 112, 15, 128, 85, 18, 209, 100, 21, 44, 391, 24, 125, 208, 27, 224, 493, 30, 341, 64, 231, 68, 175, 36, 185, 418, 39, 80, 697, 84, 215, 88, 225, 46, 329, 48, 539, 100, 153, 364, 1007, 54, 715, 56, 285, 58, 767, 120, 61, 1178, 315
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Condition gcd(a(n),n+1) = 1 ensures that a(n+1) exists.
Primes arising as absolute first differences are given in A096878.
For corresponding sequence starting (more naturally) at 1 see A096879.
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EXAMPLE
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a(8) has to be a multiple of 8; 80 is the smallest one that satisfies all conditions: 80 is coprime to 9, abs(a(7) - 80) = 73 is prime and distinct from all earlier absolute differences 2, 5, 3, 7, 13, 11. Hence a(8) = 80.
a(9) has to be a multiple of 9; 9 is the smallest one that satisfies all conditions: 9 is coprime to 10, abs(a(8) - 9) = 71 is prime and distinct from all earlier absolute differences 2, 5, 3, 7, 13, 11, 73. Hence a(9) = 9.
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PROGRAM
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(PARI) {print1(a=2, ", "); v=Set([]); for(n=2, 63, k=1; b=1; while(b, m=k*n; p=abs(m-a); if(gcd(m, n+1)==1&&isprime(p)&&setsearch(v, p)==0, v=setunion(v, Set(p)); print1(m, ", "); a=m; b=0, k++)))}
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CROSSREFS
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Cf. A096878, A096879.
Sequence in context: A047348 A093859 A115905 this_sequence A058885 A022428 A096186
Adjacent sequences: A096131 A096132 A096133 this_sequence A096135 A096136 A096137
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 04 2004
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EXTENSIONS
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Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 14 2004
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