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A355329 Least increasing sequence of primes such that a(n) - 1 is a multiple of 6*n.

%I A355329 #13 Jul 05 2022 06:17:03
%S A355329 7,13,19,73,151,181,211,241,271,421,463,577,859,1009,1171,1249,1327,
%T A355329 1621,2053,2161,2269,2377,3037,3169,3301,3433,3727,4201,5569,5581,
%U A355329 5953,6337,6733,7549,7561,7993,9103,9349,9829,10321,10333,10837,11353,11617,12421,12697,12973,13249,14407,15601
%N A355329 Least increasing sequence of primes such that a(n) - 1 is a multiple of 6*n.
%C A355329 a(n) is the least prime == 1 mod (6*n) and (for n >= 2) greater than a(n-1).
%H A355329 Robert Israel, <a href="/A355329/b355329.txt">Table of n, a(n) for n = 1..10000</a>
%e A355329 a(5) = 151 because 151 is prime, 151-1 = 150 is divisible by 6*5, and 151 > a(4) = 73.
%p A355329 A:= Vector(100):
%p A355329 A[1]:= 7:
%p A355329 for n from 2 to 100 do
%p A355329   for k from floor((A[n-1]-1)/(6*n))+1  do
%p A355329     p:= 6*n*k+1;
%p A355329     if isprime(p) then A[n]:= p; break fi
%p A355329 od od:
%p A355329 convert(A,list);
%t A355329 a[n_] := a[n] = Module[{p = If[n == 1, 2, NextPrime[a[n - 1]]]}, While[!Divisible[p - 1, 6*n], p = NextPrime[p]]; p]; Array[a, 50] (* _Amiram Eldar_, Jun 29 2022 *)
%o A355329 (Python)
%o A355329 from itertools import count, islice
%o A355329 from sympy import nextprime
%o A355329 def A355329_gen(): # generator of terms
%o A355329     p = 2
%o A355329     for m in count(6,6):
%o A355329         while q:=(p-1)%m:
%o A355329             p = nextprime(p+m-q-1)
%o A355329         yield p
%o A355329         p = nextprime(p)
%o A355329 A355329_list = list(islice(A355329_gen(),30)) # _Chai Wah Wu_, Jun 30 2022
%Y A355329 Cf. A070850.
%K A355329 nonn
%O A355329 1,1
%A A355329 _J. M. Bergot_ and _Robert Israel_, Jun 29 2022