OFFSET
1,1
COMMENTS
If x and y are two consecutive prime numbers (x < y), Euclid's algorithm gives integers t and d such that tx+dy = 1 = gcd(x, y). The algorithm "Anomalia" gives t and d such that |t+d| is as small as possible (it is often = 1). The prime number x is 'anomalous' iff |t+d| > 1 for x and y.
That is, primes p such that neither q-1 nor q+1 is divisible by q-p, where q is the next prime larger than p. - Charles R Greathouse IV, Aug 20 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
Conjecture: a(n) ~ n log n. - Charles R Greathouse IV, Aug 20 2017
EXAMPLE
a(1) = 199 because -88*199+83*211 = 1, |-88+83| = 5 > 1;
|tx+dy| = 1 for all primes x < 199 (when t and d are determined by the algorithm "Anomalia")
PROG
{ALGORITHM "Anomalia" in pseudo language} INPUT x, y {positive integers} m := x, n := y, b := 0, d := 1, p := 1, t := 0 WHILE m <> 0 DO q := n DIV m h := m, m := n-q*m, n := h h := b, b := d-q*b, d := h h := p, p := t-q*p, t := h WRITE - The gcd of the numbers is WRITE n = tx+dy {this is 1 for consecutive primes}
(PARI) is(x)=if(!isprime(x), return(0)); my(y=nextprime(x+1), d=y-x); (y-1)%d && (y+1)%d \\ Charles R Greathouse IV, Aug 20 2017
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Pahikkala Jussi, May 11 2005
STATUS
approved