A284262 a(n) = where A284259 for the first time obtains value n (positions of its records).

1, 2, 6, 105, 5005, 85085, 1616615, 37182145, 6685349671, 247357937827, 10141675450907, 436092044389001, 20496326086283047, 9156001667401012567, 558516101711461766587, 37420578814667938361329, 2656861095841423623654359, 193950859996423924526768207, 15322117939717490037614688353, 1271735788996551673122019133299

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..335

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

Adjacent sequences: A284259 A284260 A284261 * A284263 A284264 A284265

Keyword

nonn

Author

Antti Karttunen, Mar 24 2017

Status

approved