A371024
a(n) is the least prime p such that p + 4*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.
Original entry on oeis.org
2, 3, 29, 5, 23, 269, 272879, 149, 61463, 929, 7426253, 2609, 233, 59, 78977932125503
Offset: 1
-
f:= proc(p) local k;
for k from 1 while isprime(p+k*(k+1)*4) do od:
k
end proc:
A:= Vector(12): count:= 0:
for i from 1 while count < 12 do
v:= f(ithprime(i));
if A[v] = 0 then count:= count+1; A[v]:= ithprime(i) fi
od:
convert(A,list);
-
Table[p=1;m=4;Monitor[Parallelize[While[True,If[And[MemberQ[PrimeQ[Table[p+m*k*(k+1),{k,0,n-1}]],False]==False,PrimeQ[p+m*n*(n+1)]==False],Break[]];p++];p],p],{n,1,10}]
-
isok(p, n) = for (k=0, n-1, if (! isprime(p + 4*k*(k+1)), return(0))); return (!isprime(p + 4*n*(n+1)));
a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p; \\ Michel Marcus, Mar 12 2024
-
use ntheory qw(:all); sub a { my $n = $[0]; my $lo = 2; my $hi = 2*$lo; while (1) { my @terms = grep { !is_prime($ + 4*$n*($n+1)) } sieve_prime_cluster($lo, $hi, map { 4*$*($+1) } 1 .. $n-1); return $terms[0] if @terms; $lo = $hi+1; $hi = 2*$lo; } }; $| = 1; for my $n (1..100) { print a($n), ", " }; # Daniel Suteu, Dec 17 2024
-
from sympy import isprime, nextprime
from itertools import count, islice
def f(p):
k = 1
while isprime(p+4*k*(k+1)): k += 1
return k
def agen(verbose=False): # generator of terms
adict, n, p = dict(), 1, 1
while True:
p = nextprime(p)
v = f(p)
if v not in adict:
adict[v] = p
if verbose: print("FOUND", v, p)
while n in adict:
yield adict[n]; n += 1
print(list(islice(agen(), 14))) # Michael S. Branicky, Apr 12 2024
A376675
a(n) is the least prime p such that p + 7*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.
Original entry on oeis.org
2, 3, 59, 5, 89, 599, 3329, 617, 269, 21107, 9833477, 19497833669, 215830859597, 111338387, 251704297005767, 17
Offset: 1
-
f:= proc(p) local k;
for k from 1 while isprime(p+k*(k+1)*7) do od:
k
end proc:
A:= Vector(12): count:= 0:
for i from 1 while count < 12 do
v:= f(ithprime(i));
if A[v] = 0 then count:= count+1; A[v]:= ithprime(i) fi
od:
convert(A,list);
-
Table[p=1;m=7;Monitor[Parallelize[While[True,If[And[MemberQ[PrimeQ[Table[p+m*k*(k+1),{k,0,n-1}]],False]==False,PrimeQ[p+m*n*(n+1)]==False],Break[]];p++];p],p],{n,1,10}]
-
isok(p, n) = for (k=0, n-1, if (! isprime(p + 7*k*(k+1)), return(0))); return (!isprime(p + 7*n*(n+1)));
a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p;
-
use ntheory qw(:all); sub a { my $n = $[0]; my $lo = 2; my $hi = 2*$lo; while (1) { my @terms = grep { !is_prime($ + 7*$n*($n+1)) } sieve_prime_cluster($lo, $hi, map { 7*$*($+1) } 1 .. $n-1); return $terms[0] if @terms; $lo = $hi+1; $hi = 2*$lo; } }; $| = 1; for my $n (1..100) { print a($n), ", " }; # Daniel Suteu, Oct 04 2024
A378839
a(n) is the least prime p such that p + 8*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.
Original entry on oeis.org
2, 3, 151, 181, 13, 811, 23671, 92221, 45417481, 5078503, 4861, 20379346831, 12180447943, 31, 10347699089473
Offset: 1
-
f:= proc(p) local k;
for k from 1 while isprime(p+k*(k+1)*8) do od:
k
end proc:
A:= Vector(12): count:= 0:
for i from 1 while count < 12 do
v:= f(ithprime(i));
if A[v] = 0 then count:= count+1; A[v]:= ithprime(i) fi
od:
convert(A,list);
-
Table[p=1;m=8;Monitor[Parallelize[While[True,If[And[MemberQ[PrimeQ[Table[p+m*k*(k+1),{k,0,n-1}]],False]==False,PrimeQ[p+m*n*(n+1)]==False],Break[]];p++];p],p],{n,1,10}]
-
isok(p, n) = for (k=0, n-1, if (! isprime(p + 8*k*(k+1)), return(0))); return (!isprime(p + 8*n*(n+1)));
a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p;
-
use ntheory qw(:all); sub a { my $n = $[0]; my $lo = 2; my $hi = 2*$lo; while (1) { my @terms = grep { !is_prime($ + 8*$n*($n+1)) } sieve_prime_cluster($lo, $hi, map { 8*$*($+1) } 1 .. $n-1); return $terms[0] if @terms; $lo = $hi+1; $hi = 2*$lo; } }; $| = 1; for my $n (1..100) { print a($n), ", " }; #
A378841
a(n) is the least prime p such that p + 9*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.
Original entry on oeis.org
2, 11, 13, 5, 19, 173, 3163, 83, 21013, 878359, 3676219, 239, 43, 5201390418463, 86927887467919
Offset: 1
-
f:= proc(p) local k;
for k from 1 while isprime(p+k*(k+1)*9) do od:
k
end proc:
A:= Vector(12): count:= 0:
for i from 1 while count < 12 do
v:= f(ithprime(i));
if A[v] = 0 then count:= count+1; A[v]:= ithprime(i) fi
od:
convert(A,list);
-
Table[p=1;m=9;Monitor[Parallelize[While[True,If[And[MemberQ[PrimeQ[Table[p+m*k*(k+1),{k,0,n-1}]],False]==False,PrimeQ[p+m*n*(n+1)]==False],Break[]];p++];p],p],{n,1,10}]
-
isok(p, n) = for (k=0, n-1, if (! isprime(p + 9*k*(k+1)), return(0))); return (!isprime(p + 9*n*(n+1)));
a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p;
-
use ntheory qw(:all); sub a { my $n = $[0]; my $lo = 2; my $hi = 2*$lo; while (1) { my @terms = grep { !is_prime($ + 9*$n*($n+1)) } sieve_prime_cluster($lo, $hi, map { 9*$*($+1) } 1 .. $n-1); return $terms[0] if @terms; $lo = $hi+1; $hi = 2*$lo; } }; $| = 1; for my $n (1..100) { print a($n), ", " }; #
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