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 A161795 The multiplicity of successive elements of sequence A005250 (increasing prime gaps) as they occur in A161794, the largest prime gap less than (n+1)^2. 0
 1, 1, 2, 4, 2, 12, 7, 3, 3, 61, 28, 15, 37, 217, 206, 8, 93, 460, 4, 253, 738 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Sequence A161794 suggests the size of prime gaps grows slower than the size of square intervals, lending credence to Legendre's conjecture. LINKS Table of n, a(n) for n=1..21. EXAMPLE A161794 begins 1, 2, 4, 4, 6, 6, 6, 6, ... that is, 1 one, 1 two, 2 four, 4 six, ... so this sequence begins 1, 1, 2, 4, ... PROG (PARI) f(n) = my(vp = primes(primepi((n+1)^2))); vecmax(vector(#vp-1, k, vp[k+1] - vp[k])); \\ A161794 lista(nn) = my(v = vector(nn, k, f(k))); my(list = List(), last = v[1], nb=1); for (n=2, #v, if (v[n] == last, nb++, listput(list, nb); nb = 1; last = v[n]; ); ); Vec(list); \\ Michel Marcus, Aug 15 2022 CROSSREFS Cf. A005250, A161794. Sequence in context: A121799 A078034 A181091 * A138770 A006018 A152666 Adjacent sequences: A161792 A161793 A161794 * A161796 A161797 A161798 KEYWORD nonn,more AUTHOR Daniel Tisdale, Jun 19 2009 EXTENSIONS a(15)-a(21) from Michel Marcus, Aug 15 2022 STATUS approved

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Last modified August 12 10:37 EDT 2024. Contains 375092 sequences. (Running on oeis4.)