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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If we remove the restriction A019565(k)^2<=P(n), every elements get doubled.
Number of distinct primes of the form d + P(n)/d, where P(n) is the nth primorial A002110(n) and d is a divisor of P(n).
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FORMULA
| a(n) = A088627(A002110(n)/2)
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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;
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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}]
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CROSSREFS
| Cf. A019565, A002110, A103785, A103786.
Sequence in context: A076651 A081410 A027677 * A032473 A084422 A175841
Adjacent sequences: A103784 A103785 A103786 * A103788 A103789 A103790
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KEYWORD
| hard,nonn
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AUTHOR
| Lei Zhou (lzhou5(AT)emory.edu), Feb 15 2005
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