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.

2, 3, 31, 43, 37, 7, 709, 8941, 1723, 163, 1801, 13, 32077430821, 313296437089, 106776242048569, 3345710409941689

Offset: 1

Author

J. M. Bergot and Robert Israel, May 27 2021

Keywords

• nonn
• more

Comments

a(n) is the least p such that p, p+10, p+10+20, ..., p+10+20+...+10*(n-1) are prime but p+10+20+...+10*n is composite.

Examples

			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.
		

Crossrefs

Cf. A164926.

Programs

Maple

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);

Mathematica

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 *)

Extensions

a(13)-a(14) from Martin Ehrenstein, May 28 2021

a(15)-a(16) from Bert Dobbelaere, Jun 07 2021