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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

Table of n, a(n) for n=1..19.

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

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