

A096134


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(n1) is a prime distinct from all earlier such differences of consecutive terms.


2



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
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OFFSET

1,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..63.


EXAMPLE

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.


PROG

(PARI) {print1(a=2, ", "); v=Set([]); for(n=2, 63, k=1; b=1; while(b, m=k*n; p=abs(ma); if(gcd(m, n+1)==1&&isprime(p)&&setsearch(v, p)==0, v=setunion(v, Set(p)); print1(m, ", "); a=m; b=0, k++)))}


CROSSREFS

Cf. A096878, A096879.
Sequence in context: A115905 A292769 A307997 * A058885 A256446 A022428
Adjacent sequences: A096131 A096132 A096133 * A096135 A096136 A096137


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Jul 04 2004


EXTENSIONS

Edited, corrected and extended by Klaus Brockhaus, Jul 14 2004


STATUS

approved



