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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 (list; graph; refs; listen; history; text; internal format)
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

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 xrange(A(n) + 1, A(n) + n + 1)])

print [a(n) for n in xrange(0, 51)] # 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 * A287935 A181036 A222854

Adjacent sequences:  A284259 A284260 A284261 * A284263 A284264 A284265

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 24 2017

STATUS

approved

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Last modified February 23 02:29 EST 2019. Contains 320411 sequences. (Running on oeis4.)