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A284262
a(n) = where A284259 for the first time obtains value n (positions of its records).
3
1, 2, 6, 105, 5005, 85085, 1616615, 37182145, 6685349671, 247357937827, 10141675450907, 436092044389001, 20496326086283047, 9156001667401012567, 558516101711461766587, 37420578814667938361329, 2656861095841423623654359, 193950859996423924526768207, 15322117939717490037614688353, 1271735788996551673122019133299
OFFSET
0,2
LINKS
FORMULA
For n > 1, a(n) = Product_{i = A284263(n)+1 .. A284263(n)+n} prime(i); a(0) = 1, a(1) = 2.
a(n) = A242378(A284263(n), A002110(n)) [shift the prime factorization of the n-th primorial A284263(n) steps towards larger primes].
Other identities. For all n >= 0:
A001221(a(n)) = A001222(a(n)) = n.
A284259(a(n)) = n.
MATHEMATICA
A[n_]:= If[n<1, 0, Block[{k=1}, While[Prime[n + k - 1] > Prime[k]^2, k++]; k - 1]]; a[n_]:=If[n<2, n + 1, Product[Prime[i], {i, A[n] + 1, A[n] + n}]]; Table[a[n], {n, 0, 51}] (* Indranil Ghosh, Mar 24 2017 *)
PROG
(Scheme) (define (A284262 n) (A242378bi (A284263 n) (A002110 n))) ;; Where A242378bi(k, n) applies prime shift A003961(n) k times. See A242378.
(PARI) A(n) = { my(k=1); if(0==n, 0, while(prime(n+k-1) > (prime(k)^2), k = k+1); (k-1)); };
a(n) = prod(i=A(n) + 1, A(n) + n, prime(i));
for(n=0, 51, print1(a(n), ", ")) \\ Indranil Ghosh, after Antti Karttunen, Mar 24 2017
(Python)
from sympy import prime
from operator import mul
from functools import reduce
def A(n):
if n<1: return 0
k=1
while prime(n + k - 1)>prime(k)**2:k+=1
return k - 1
def a(n): return n + 1 if n<2 else reduce(mul, [prime(i) for i in range(A(n) + 1, A(n) + n + 1)])
print([a(n) for n in range(21)]) # Indranil Ghosh, Mar 24 2017
CROSSREFS
Cf. A001221, A001222, A002110, A003961, A242378, A284259 (a left inverse), A284263.
Cf. also A109819.
Sequence in context: A278888 A099790 A294906 * A374006 A287935 A357090
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 24 2017
STATUS
approved