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A237196 a(n) = index j of the first composite number in the sequence prime(1)*...*prime(n-1)*prime(n+1)*...*prime(j) + prime(n). 1
4, 5, 7, 1, 4, 1, 5, 1, 1, 2, 1, 1, 9, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1, 8, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is based on a modification of Euclid's proof of the infinitude of primes.

LINKS

Table of n, a(n) for n=1..87.

Alexander Bogomolny, Infinitely many proofs that there are infinitely many primes

Alexander Bogomolny, Python program

Des MacHale, Infinitely many proofs that there are infinitely many primes, Math. Gazette, 97 (No. 540, 2013), 495-498.

EXAMPLE

This is a modification of Euclid's proof of the infinitude of primes. Instead of 1, add a prime but exclude it from the product. For example, primes: 3+2, 3*5+2, 3*5*7+2, but 3*5*7*11+2 is composite. This is the 4 at the beginning of the sequence.

PROG

(Python) see Python program link

(PARI) val(j, n) = {p = prod(k=1, j, prime(k)); if (n<=j, p = p/prime(n)); p + prime(n); }

a(n) = {j = 1; prev = 0; nb = 1; while (! isprime(newv = val(j, n)), if (newv != prev, nb++); j++; prev = newv; ); if (n==1, nb-1, nb); } \\ Michel Marcus, Apr 15 2014

CROSSREFS

Sequence in context: A298982 A112247 A319260 * A322711 A057055 A177883

Adjacent sequences:  A237193 A237194 A237195 * A237197 A237198 A237199

KEYWORD

nonn

AUTHOR

Alexander Bogomolny, Feb 04 2014

EXTENSIONS

New name, data corrected and extended by Michel Marcus, Apr 15 2014

STATUS

approved

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Last modified January 26 20:11 EST 2020. Contains 331288 sequences. (Running on oeis4.)