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 A353203 Let b be a composite number, c be the smallest composite number greater than b and coprime to b, and d = c-b. This sequence contains all b such that d is neither a prime nor a square. 1
 67613590, 72808450, 125918320, 153469030, 190281850, 229119880, 328315900, 339204910, 360203140, 395961280, 447304000, 450075340, 692309530, 844334920, 861327610, 909001390, 1029358330, 1166831380, 1178236510, 1321005400, 1344348610, 1366379080, 2035500610, 2045710810, 2156564410 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Other such terms are 18806843674476 and 18806855958880. a(n) is even. Proof: If a(n) = b is odd then c = a(n) + 1 where gcd(b, c) = 1 and d = c-b = 1 which is a square. Contradiction. - David A. Corneth, May 01 2022 LINKS Table of n, a(n) for n=1..25. EXAMPLE If b = 6, then c = 25 and d = c-b = 19 (prime), so 6 is not in the sequence. If b = 67613590, then c = 67613611, and d = c-b = 21 (neither prime nor square), so 67613590 is in the sequence. MATHEMATICA c[n_]:=Module[{k=n+1}, While[GCD[n, k]!=1||PrimeQ[k], k++]; k]; Select[Range[10^8], CompositeQ[#]&&CompositeQ[c[#]-#]&&!IntegerQ[Sqrt[c[#]-#]]&] CROSSREFS Cf. A002808, A113496, A342175. Sequence in context: A089081 A161774 A203670 * A183707 A256274 A158890 Adjacent sequences: A353200 A353201 A353202 * A353204 A353205 A353206 KEYWORD nonn AUTHOR Fausto Morales Díaz and Ivan N. Ianakiev, Apr 30 2022 STATUS approved

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Last modified December 2 23:17 EST 2023. Contains 367526 sequences. (Running on oeis4.)