This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A219953 a(1) = 1; for n>1, a(n) = smallest integer > a(n-1) such that a(n)*a(i)+1 is semiprime for all 1 <= i <= n-1. 1
 1, 3, 8, 38, 86, 318, 504, 3600, 8132, 83160, 116850, 202272, 399126, 6190086, 8756916, 25253676, 309709400, 1112878446, 1478724036 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is to A034881 as semiprimes A001358 are to primes A000040. a(20) > 6*10^9. - Giovanni Resta, Jul 26 2015 LINKS EXAMPLE a(1) = 1 by definition. a(2) = 3: 3>1, and 1*3 + 1 = 4 = 2^2 is semiprime. a(3) = 8: 8>3, and 1*8 + 1 = 9 = 3^2 is semiprime, and 3*8 + 1 = 25 = 5^2 is semiprime. a(4) = 38: 38>8, and 1*38 + 1 = 39 = 3*13 is semiprime, and 3*38 + 1 = 115 = 5*23 is semiprime, and 8*38 + 1 = 305 = 5*61 is semiprime. From Michel Marcus, Jul 26 2015: (Start) The resulting semiprimes are: 4; 9, 25; 39, 115, 305; 87, 259, 689, 3269; 319, 955, 2545, 12085, 27349; ... (End) MAPLE A219953 := proc(n)     option remember;     if n= 1 then         1;     else         for a from procname(n-1)+1 do             issp := true ;             for i from 1 to n-1 do                 if numtheory[bigomega]( a*procname(n-i)+1) = 2 then                     ;                 else                     issp := false;                     break ;                 end if;             end do:             if issp then                 return a;             end if;         end do:     end if; end proc: # R. J. Mathar, Dec 15 2012 MATHEMATICA a = {1}; Do[k = a[[n - 1]] + 1; While[! AllTrue[(k a[[n - #]] + 1) & /@ Range@ (n - 1), Total[Last /@ FactorInteger@ #] == 2 &], k++]; AppendTo[a, k], {n, 2, 13}]; a (* Michael De Vlieger, Jul 26 2015, Version 10 *) PROG (PARI) ok(v, n, k) = {v[n] = k; for (j=1, n-1, if (bigomega(1+v[n]*v[j]) != 2, return (0)); ); return (1); } lista(nn) = {print1(k=1, ", "); v = [k]; for (n=2, nn, k = v[n-1]+1; v = concat(v, k); while (! ok(v, n, k), k++); v[n] = k; print1(k, ", "); ); } \\ Michel Marcus, Jul 26 2015 CROSSREFS Cf. A030063, A001358, A034881, A219761. Sequence in context: A147523 A123981 A123985 * A286075 A089066 A099030 Adjacent sequences:  A219950 A219951 A219952 * A219954 A219955 A219956 KEYWORD nonn,more AUTHOR Jonathan Vos Post, Dec 01 2012 EXTENSIONS a(14)-a(17) from Luke March, Jul 26 2015 a(18)-a(19) from Giovanni Resta, Jul 26 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)