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 A336520 Primes in Pi: a(n) is the smallest prime factor of A090897(n) that does not appear in earlier terms of A090897, or 1, if no such factor exists. 2
 3, 2, 53, 379, 58979, 161923, 2643383, 1746893, 6971, 5, 17, 1499, 11, 1555077581737, 297707, 4733, 37, 126541, 2130276389911155737, 1429, 71971, 383, 61, 1559, 29, 193, 12073, 698543, 157, 20289606809, 23687, 1249, 59, 2393, 251, 101, 15827173, 82351, 661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Inspired by a comment of Mario Cortés in A090897, who suggests that 1 might not appear in this sequence. Differs from A336519 for n = 4, 16, 73, 83, 90, .... a(n) is not 1 for the first 2000 terms. We can prove that a(n) has a prime factor p that does not divide LCM(A090897(1), ..., A090897(n-1)) without using prime number factorization. The method is explained in the link below. - David A. Corneth, Aug 22 2020 LINKS Table of n, a(n) for n=1..39. Peter Luschny, Prime factorization for n = 1..100. David A. Corneth, Explanation of a method to determine the primality of a(n). Comes with example and PARI program. EXAMPLE [ 1] 3, {3} -> 3; [ 2] 14, {2, 7} -> 2; [ 3] 159, {3, 53} -> 53; [ 4] 2653, {7, 379} -> 379; [ 5] 58979, {58979} -> 58979; [ 6] 323846, {2, 161923} -> 161923; [ 7] 2643383, {2643383} -> 2643383; [ 8] 27950288, {2, 1746893} -> 1746893; [ 9] 419716939, {6971, 60209} -> 6971; [10] 9375105820, {2, 5, 1163, 403057} -> 5. PROG (SageMath) def Select(item, Selected): return next((x for x in item if not (x in Selected)), 1) def PiPart(n): return floor(pi * 10^(n * (n + 1) // 2 - 1)) % 10^n def A336520List(len): prev = []; ret = [] for n in range(1, len + 1): p = prime_factors(PiPart(n)) ret.append(Select(p, prev)) prev.extend(p) return ret print(A336520List(39)) # Query function of David A. Corneth to determine if a(n) is prime. def LcmPiPart(n): return lcm([PiPart(n) for n in (1..n)]) def is_an_prime(n): lcmpi = LcmPiPart(n - 1) lm, m = 1, PiPart(n) while lm != m: lm, m = m, lcm(lcmpi, m) // lcmpi return m > 1 CROSSREFS Cf. A090897, A336519 (variant). Sequence in context: A104254 A336519 A231576 * A190286 A063513 A265635 Adjacent sequences: A336517 A336518 A336519 * A336521 A336522 A336523 KEYWORD nonn,base AUTHOR Peter Luschny, Aug 22 2020 STATUS approved

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Last modified May 18 02:01 EDT 2024. Contains 372615 sequences. (Running on oeis4.)