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 A303436 Primes p such that all the composite numbers between p and its next prime have no more than 2 distinct prime factors. 0
 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 43, 47, 53, 71, 79, 97, 107, 157, 191, 223, 431, 499, 673, 1151, 1213, 2591, 51199, 139967, 472391, 703123, 786431, 995327, 57395627, 63700991, 169869311, 4076863487, 10871635967 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Supersequence of A078883. Terms that are not there: 2, 7, 13, 19, 23, 31, 37, 43, 47, 53, 79, 97, 157, 223, 499, 673, 1213, 51199, 703123, ... 5*10^11 < a(39) <= 2348273369087. - Giovanni Resta, Apr 26 2018 LINKS Table of n, a(n) for n=1..38. EXAMPLE 157 is in the sequence since it is a prime, and the composite numbers between it and its next prime, 163, have only 2 distinct prime factors: 158 = 2*79, 159 = 3*53, 160 = 2^5*5, 161 = 7*23, and 162 = 2*3^4. MATHEMATICA b[n_] := Max[Map[PrimeNu, Range[n + 1, NextPrime[n] - 1]]]; c[n_] := b[Prime[n]]; a={}; Do[If[c[n] < 3, AppendTo[a, Prime[n]]], {n, 1, 10^7}]; a PROG (PARI) isok(p) = {if (isprime(p), for(c=p+1, nextprime(p+1)-1, if (omega(c) != 2, return(0)); ); return (1); ); } \\ Michel Marcus, Apr 26 2018 CROSSREFS Cf. A078883. Sequence in context: A006514 A216286 A086983 * A334797 A229060 A219528 Adjacent sequences: A303433 A303434 A303435 * A303437 A303438 A303439 KEYWORD nonn,more AUTHOR Amiram Eldar, Apr 24 2018 EXTENSIONS a(36) from Michel Marcus, Apr 26 2018 a(37)-a(38) from Giovanni Resta, Apr 26 2018 STATUS approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)