A047980 a(n) is smallest difference d of an arithmetic progression dk+1 whose first prime occurs at the n-th position.
1, 3, 24, 7, 38, 17, 184, 71, 368, 19, 668, 59, 634, 167, 512, 757, 1028, 197, 1468, 159, 3382, 799, 4106, 227, 10012, 317, 7628, 415, 11282, 361, 38032, 521, 53630, 3289, 37274, 2633, 63334, 1637, 34108, 1861, 102296, 1691, 119074, 1997, 109474, 2053
Offset: 1
Keywords
Examples
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
Links
- Jon E. Schoenfield, Table of n, a(n) for n = 1..150 (terms 1..72 from Robert Israel)
- Jon E. Schoenfield, Terms <= 5*10^8: Table of n, a(n) for n = 1..406, with -1 for each term > 5*10^8
- Index entries for sequences related to primes in arithmetic progressions
Programs
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MATLAB
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
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Maple
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 -
Mathematica
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 *)
Formula
a(n) = min{k | A034693(k) = n}.
Comments