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 A074172 Smaller of two consecutive numbers of the form p^2*q where p and q are primes. 11
 44, 75, 98, 116, 147, 171, 244, 332, 387, 507, 548, 603, 604, 724, 844, 908, 931, 963, 1075, 1083, 1251, 1324, 1412, 1467, 1556, 1587, 1675, 1772, 2523, 2524, 2636, 2644, 2763, 3283, 3356, 3411, 3508, 3788, 3987, 4075, 4203, 4204, 4418, 4491, 4804, 4868 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Robert Israel, Dec 06 2018: (Start) There are four forms of terms, for odd primes p,q,r: 4*p where 4*p+1 = q^2*r, r == 1 (mod 4) 2*p^2 where 2*p^2+1 = q^2*r, r == 3 (mod 4) p^2*q where p^2*q+1 = 2*r^2, q == 1 (mod 4) p^2*q where p^2*q+1 = 4*r, q == 3 (mod 4). Are there infinitely many terms of each type? (End) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 44 is a member as 44 = 2^2*11 and 45 = 3^2*5. MAPLE filter:= proc(n) local F; F:= map(t -> t[2], ifactors(n)[2]); F = [2, 1] or F = [1, 2] end proc: A054753:= select(filter, {\$1..10000}): sort(convert(A054753 intersect map(`-`, A054753, 1), list)); # Robert Israel, Dec 06 2018 MATHEMATICA lst={}; Do[f1=FactorInteger[n]; If[Sort[Transpose[f1][[2]]]=={1, 2}, f2=FactorInteger[n+1]; If[Sort[Transpose[f2][[2]]]=={1, 2}, AppendTo[lst, n]]], {n, 3, 10000}]; lst PROG (PARI) isok1(n) = vecsort(factor(n)[, 2]) == [1, 2]~; isok(n) = isok1(n) && isok1(n+1); \\ Michel Marcus, Sep 20 2017 CROSSREFS Cf. A054753, A074173, A074174, A178032, A308683, A141621. Sequence in context: A348076 A348345 A049103 * A039386 A043209 A043989 Adjacent sequences: A074169 A074170 A074171 * A074173 A074174 A074175 KEYWORD nonn AUTHOR Amarnath Murthy, Aug 30 2002 EXTENSIONS More terms from T. D. Noe, Oct 04 2004 STATUS approved

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Last modified April 14 13:30 EDT 2024. Contains 371661 sequences. (Running on oeis4.)