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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 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.)