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), ", " }; #
A344736
a(n) is the least p such that p + 5*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.
Original entry on oeis.org
2, 3, 31, 43, 37, 7, 709, 8941, 1723, 163, 1801, 13, 32077430821, 313296437089, 106776242048569, 3345710409941689
Offset: 1
a(4) = 43 because 43, 43+10=53, 53+20=73, 73+30=103 are prime but 103+40=143 is composite, and no number smaller than 43 works.
-
f:= proc(p) local k;
for k from 1 while isprime(p+k*(k+1)*5) 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=5;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}] (* J.W.L. (Jan) Eerland, Mar 08 2024 *)
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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