This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
If n = 7, the smallest prime in the sequence 8, 15, 22, 29, ... is 29, so a(7) = 29.
a034694 n = until ((== 1) . a010051) (+ n) (n + 1) -- Reinhard Zumkeller, Dec 17 2013
a[n_] := Block[{k = 1}, If[n == 1, 2, While[Mod[Prime@k, n] != 1, k++ ]; Prime@k]]; Array[a, 64] (* Robert G. Wilson v, Jul 08 2006 *)
With[{prs=Prime[Range[200]]},Flatten[Table[Select[prs,Mod[#-1,n]==0&,1],{n,70}]]] (* Harvey P. Dale, Sep 22 2021 *)
a(n)=if(n<0,0,s=1; while((prime(s)-1)%n>0,s++); prime(s))
For n=2, the sequence with d=1 is 2,3,4,5,... with the prime 2 for k=1. The sequence with d=2 is 3,5,7,9,... with the prime 3 for k=1. The sequence with d=3 is 4,7,10,13,... with the prime 7 for k=2. So a(n)=3. - _Michael B. Porter_, Mar 18 2019
function [ A ] = A047980( P, N ) % Get values a(i) for i <= N with a(i) <= P/i % using primes <= P. % Returned entries A(n) = 0 correspond to unknown a(n) > P/n Primes = primes(P); A = zeros(1,N); Ds = zeros(1,P); for p = Primes ns = [1:N]; ns = ns(mod((p-1) * ones(1,N), ns) == 0); newds = (p-1) ./ns; ns = ns(A(ns) == 0); ds = (p-1) ./ ns; q = (Ds(ds) == 0); A(ns(q)) = ds(q); Ds(newds) = 1; end end % Robert Israel, Jan 25 2016
N:= 40: # to get a(n) for n <= N
count:= 0:
p:= 0:
Ds:= {1}:
while count < N do
p:= nextprime(p);
ds:= select(d -> (p-1)/d <= N, numtheory:-divisors(p-1) minus Ds);
for d in ds do
n:= (p-1)/d;
if not assigned(A[n]) then
A[n]:= d;
count:= count+1;
fi
od:
Ds:= Ds union ds;
od:
seq(A[i],i=1..N); # Robert Israel, Jan 25 2016
With[{s = Table[k = 1; While[! PrimeQ[k n + 1], k++]; k, {n, 10^6}]}, TakeWhile[#, # > 0 &] &@ Flatten@ Array[FirstPosition[s, #] /. k_ /; MissingQ@ k -> {0} &, Max@ s]] (* Michael De Vlieger, Aug 01 2017 *)
a(2)=38 because A034693(38) = 2*2+1 = 5 is the first 5; 5*38+1 = 191 is the first prime. The successive progressions in which the first prime appears at position 5 are as follows: 38k+1, 62k+1, 164k+1. 2nd example: a(20)=102296 because. The first 41 appears in A034693 at this index. Also 102296*(2*20+1)+1 = 102296*41+1 = 4194137 is the first prime in {102296k+1}. The next progression with this position of prime emergence is 109946k+1 (the corresponding prime is 4507787).
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