A087714
Primes p = prime(i) such that p(i)# - p(i+1) and p(i)# + p(i+1) are both primes, where p# = A002110.
Original entry on oeis.org
2*3*5-7 = 23 is prime, 2*3*5+7 = 37 is prime.
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isok(p) = {if (isprime(p), my(pp = prod(k=1, primepi(p), prime(k)), q = nextprime(p+1)); isprime(pp-q) && isprime(pp+q););} \\ Michel Marcus, Sep 20 2019
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my(pr=1); forprime(p=1, , pr=pr*p; if(ispseudoprime(pr-nextprime(p+1)) && ispseudoprime(pr+nextprime(p+1)), print1(p, ", "))) \\ Felix Fröhlich, Sep 20 2019
A087715
Table read by rows where i-th row consists of primes P of the form P=j*P(i)# -1 or P=j*P(i)# +1 with 0 < j < P(i+1). Here P(r)# = A002110.
Original entry on oeis.org
3, 3, 5, 5, 7, 11, 13, 17, 19, 23, 29, 31, 59, 61, 89, 149, 151, 179, 181, 211, 419, 421, 631, 839, 1049, 1051, 1259, 1471, 1889, 2099, 2309, 2311, 4621, 9239, 9241, 11549, 11551, 13859, 18481, 20789, 23099, 25409, 25411, 30029, 90089, 120121, 150151
Offset: 0
Table begins:
3,3,5,
5,7,11,13,17,19,23,
29,31,59,61,89,149,151,179,181,
211,419,421,631,839,1049,1051,1259,1471,1889,2099,
2309,2311,4621,9239,9241,11549,11551,13859,18481,20789,23099,25409,25411
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{for(i=1,6, p=prod(j=1,i, prime(j)); for(j=1, prime(i+1)-1, c=j*p; if(isprime(c-1),print1(c-1 ",")); if(isprime(c+1),print1(c+1 ",")); ););}
A087716
Base-2 pseudoprimes (see A001567) of the form j*p(i)# - p(k) or j*p(i)# + p(k), p(i) and p(k) primes with p(i) < p(k) < p(i+1)^2 and 0 < j < p(i+1).
Original entry on oeis.org
341, 1387, 2047, 4681, 13747
Offset: 1
2*7# - 79 = 341,
7*7# - 83 = 1387,
10*7# - 53 = 2047,
2*11# + 61 = 4681,
6*11# - 113 = 13747,
13*7# - 29 = 2701.
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lst(lim)=my(p=2,P=1,v=List());forprime(q=3,lim,P*=p;forprime(r=q, q^2, for(j=1,q-1,if(j*P-r>340&&psp(j*P-r),listput(v,j*P-r)); if(psp(j*P+r),listput(v,j*P+r))));p=q);vecsort(Vec(v),,8) \\ Charles R Greathouse IV, Apr 12 2012
Showing 1-3 of 3 results.
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