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 A342175 a(n) is the difference between the n-th composite number and the smallest larger composite to which it is relatively prime. 1
 5, 19, 1, 1, 11, 13, 1, 1, 5, 7, 1, 1, 3, 1, 1, 1, 1, 5, 19, 1, 1, 1, 1, 13, 1, 1, 9, 13, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 17, 1, 1, 1, 1, 19, 1, 1, 11, 5, 1, 1, 1, 1, 7, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 19, 1, 1, 11, 13, 1, 1, 5, 7, 1, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: The only nonprime terms are squares (based on checking the first 2 million terms). - Ivan N. Ianakiev, Mar 28 2021 LINKS FORMULA a(n) = A113496(n) - A002808(n). - Jon E. Schoenfield, Mar 04 2021 EXAMPLE The first composite number is 4, and the smallest larger composite to which it is coprime is 9, so a(1) = 9 - 4 = 5. The second composite number is 6, and the smallest larger composite to which it is coprime is 25, so a(2) = 25 - 6 = 19. MATHEMATICA Table[Block[{k = 1}, While[Nand[GCD[#, k] == 1, CompositeQ[# + k]], k++]; k] &@ FixedPoint[n + PrimePi@ # + 1 &, n + PrimePi@ n + 1], {n, 83}] (* Michael De Vlieger, Mar 19 2021 *) PROG (PARI) lista(nn) = {forcomposite(c=1, nn, my(x=c+1); while (isprime(x) || (gcd(x, c) != 1), x++); print1(x - c, ", "); ); } \\ Michel Marcus, Mar 04 2021 (Python) from sympy import isprime, gcd, composite def A342175(n):     m = composite(n)     k = m+1     while gcd(k, m) != 1 or isprime(k):         k += 1     return k-m # Chai Wah Wu, Mar 28 2021 CROSSREFS Cf. A002808, A113496. Sequence in context: A347670 A139237 A317541 * A258080 A318181 A274995 Adjacent sequences:  A342172 A342173 A342174 * A342176 A342177 A342178 KEYWORD nonn AUTHOR William C. Laursen, Mar 04 2021 STATUS approved

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Last modified January 23 15:33 EST 2022. Contains 350514 sequences. (Running on oeis4.)