The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322271 Smallest multiplication factors f, prime or 1, for all b (mod 24), coprime to 24, so that b*f is a nonzero square mod 8 and mod 3. 7
1, 5, 7, 11, 13, 17, 19, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See sequence A322269 for further explanations. This sequence is related to A322269(2).
The sequence is periodic, repeating itself after phi(24) terms. Its largest term is 23, which is A322269(2). In order to satisfy the conditions, both f and b must be coprime to 24.
The b(n) corresponding to each a(n) is A007310(n).
In this case, the sequence is trivial, since each term is being multiplied by itself. The next related sequence, A322272, corresponding to A322269(3), already has several nontrivial terms.
LINKS
EXAMPLE
The 4th number coprime to 24 is 11. a(4) is 11, because 11 is the smallest prime by which we can multiply 11, so that the product (11*11 = 121) is a square mod 8 and mod 3.
PROG
(PARI)
QresCode(n, nPrimes) = {
code = bitand(n, 7)>>1;
for (j=2, nPrimes,
x = Mod(n, prime(j));
if (issquare(x), code += (1<<j));
);
return (code);
}
QCodeArray(n) = {
totalEntries = 1<<(n+1);
f = vector(totalEntries);
f[totalEntries-3] = 1; \\ 1 always has the same code: ...111100
counter = 1;
forprime(p=prime(n+1), +oo,
code = QresCode(p, n);
if (f[code+1]==0,
f[code+1]=p;
counter += 1;
if (counter==totalEntries, return(f));
)
)
}
sequence(n) = {
f = QCodeArray(n);
primorial = prod(i=1, n, prime(i));
entries = eulerphi(4*primorial);
a = vector(entries);
i = 1;
forstep (x=1, 4*primorial-1, 2,
if (gcd(x, primorial)==1,
a[i] = f[QresCode(x, n)+1];
i += 1;
);
);
return(a);
}
\\ sequence(2) returns A322271, sequence(3) returns A322272, ... sequence(6) returns A322275.
CROSSREFS
Sequence in context: A320048 A246351 A272260 * A306289 A136801 A106571
KEYWORD
nonn,fini,full
AUTHOR
Hans Ruegg, Dec 01 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 20 02:53 EDT 2024. Contains 372703 sequences. (Running on oeis4.)