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A103787 a(n) = number of k's that make primorial P(n)/A019565(k)+A019565(k) prime, A019565(k)^2<=P(n). 3
1, 2, 4, 8, 12, 21, 40, 70, 117, 263, 450, 703, 1385, 2423, 5501, 8617, 18249, 29352, 61970, 103568, 209309, 404977, 853279, 1609502, 3008915, 5342983, 10287184, 19087437, 38498011, 78520137, 145642314 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If we remove the restriction A019565(k)^2<=P(n), every term gets doubled.

Number of distinct primes of the form d + P(n)/d, where P(n) is the n-th primorial A002110(n) and d is a divisor of P(n).

LINKS

Table of n, a(n) for n=1..31.

FORMULA

a(n) = A088627(A002110(n)/2).

EXAMPLE

P(1)=2, A019565(0)=1, 2/1+1=3 is prime, a(1)=1;

P(2)=6, A019565(0)=1, 6/1+1=7; A019565(1)=2, 6/2+2=5; so a(2)=2.

MATHEMATICA

npd = 1; Do[npd = npd*Prime[n]; tn = 0; tt = 1; cp = npd/tt + tt; ct = 0; While[IntegerQ[cp], If[(cp >= (tt*2)) && PrimeQ[cp], ct = ct + 1]; tn = tn + 1; tt = 1; k1 = tn; o = 1; While[k1 > 0, k2 = Mod[k1, 2]; If[k2 == 1, tt = tt*Prime[o]]; k1 = (k1 - k2)/2; o = o + 1]; cp = npd/tt + tt]; Print[ct], {n, 1, 22}]

Table[ps=Prime[Range[n]]; cnt=0; Do[b=IntegerDigits[i, 2, n]; p=Times@@(ps^b) + Times@@(ps^(1-b)); If[PrimeQ[p], cnt++], {i, 0, 2^(n-1)-1}]; cnt, {n, 22}]

CROSSREFS

Cf. A002110, A019565, A103785, A103786.

Sequence in context: A081410 A217694 A027677 * A032473 A084422 A175841

Adjacent sequences:  A103784 A103785 A103786 * A103788 A103789 A103790

KEYWORD

hard,nonn

AUTHOR

Lei Zhou, Feb 15 2005

EXTENSIONS

a(28)-a(31) from James G. Merickel, Aug 07 2015

STATUS

approved

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Last modified February 23 04:23 EST 2019. Contains 320411 sequences. (Running on oeis4.)