

A047980


a(n) is smallest difference d of an arithmetic progression dk+1 whose first prime occurs at the nth position.


3



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
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OFFSET

1,2


COMMENTS

Definition involves two minimal conditions: (1) the first prime (as in A034693) and (2) dk+1 sequences were searched with minimal d. Present terms are the first ones in sequences analogous to A034780, A034782A034784, A006093 (called there K(n,m)).


LINKS



FORMULA



EXAMPLE

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


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 > (p1)/d <= N, numtheory:divisors(p1) minus Ds);
for d in ds do
n:= (p1)/d;
if not assigned(A[n]) then
A[n]:= d;
count:= count+1;
fi
od:
Ds:= Ds union ds;
od:


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 *)


PROG

(MATLAB)
% 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((p1) * ones(1, N), ns) == 0);
newds = (p1) ./ns;
ns = ns(A(ns) == 0);
ds = (p1) ./ ns;
q = (Ds(ds) == 0);
A(ns(q)) = ds(q);
Ds(newds) = 1;
end


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



