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 A351863 Numbers k with at least one divisor, d, such that k-d is prime. 1
 3, 4, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 30, 32, 34, 38, 42, 44, 46, 48, 54, 58, 60, 62, 68, 72, 74, 80, 82, 84, 86, 90, 94, 98, 102, 104, 106, 108, 110, 114, 118, 122, 128, 132, 134, 138, 140, 142, 146, 150, 152, 158, 164, 166, 168, 174, 178, 180, 182, 192, 194, 198, 200, 202 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..64. FORMULA Apparently, a(n) = 2*(A179182(n-1) + 1) for n >= 2. - Hugo Pfoertner, Feb 23 2022 EXAMPLE 4 is in the sequence since 4-(1)=3, 4-(2)=2, 4-(4)=0, and at least one of 3,2,0 is prime. 56 is not in the sequence since the divisors of 56 are 1, 2, 4, 7, 8, 14, 28, 56, and none of 56-1, 56-2, 56-4, ... etc. are prime (i.e., none of 55, 54, 52, 49, 48, 42, 28, 0 are prime). MATHEMATICA q[n_] := AnyTrue[Divisors[n], PrimeQ[n - #] &]; Select[Range[200], q] (* Amiram Eldar, Feb 22 2022 *) PROG (PARI) isok(k) = sumdiv(k, d, isprime(k-d)) >= 1; \\ Michel Marcus, Feb 22 2022 (PARI) is(n) = isprime(n-1) || (n%2 == 0 && isprime(n/2)) \\ David A. Corneth, Feb 22 2022 (Python) from sympy import divisors, isprime def ok(n): return any(isprime(n-d) for d in divisors(n)) print([k for k in range(203) if ok(k)]) # Michael S. Branicky, Feb 22 2022 CROSSREFS Cf. A242932. Union of A008864 and A100484. Sequence in context: A156624 A341340 A242932 * A025201 A071259 A231405 Adjacent sequences: A351860 A351861 A351862 * A351864 A351865 A351866 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Feb 22 2022 STATUS approved

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)