A087715 -id:A087715 - cp's OEIS frontend

A087714 Primes p = prime(i) such that p(i)# - p(i+1) and p(i)# + p(i+1) are both primes, where p# = A002110.

5, 13, 19, 367

Offset: 1

Pierre CAMI, Sep 28 2003

Conjecture: there are only 4 primes in this sequence.

			2*3*5-7 = 23 is prime, 2*3*5+7 = 37 is prime.

Cf. A087715, A087716, A087728.

Cf. A002110.

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

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

A087716 Base-2 pseudoprimes (see A001567) of the form jp(i)# - p(k) or jp(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

Pierre CAMI, Sep 29 2003

Conjecture: sequence has only 5 terms. This has been checked for all i <= 150.

			   2*7#  -  79 =   341,
   7*7#  -  83 =  1387,
  10*7#  -  53 =  2047,
   2*11# +  61 =  4681,
   6*11# - 113 = 13747,
  13*7#  -  29 =  2701.

Index entries for sequences related to pseudoprimes

Cf. A001567, A087714, A087715, A087728.

# denotes primorials; see A002110.

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

Edited by David Wasserman, Apr 13 2006

A132240 Primes congruent to {1, 29} mod 30.

Original entry on oeis.org

29, 31, 59, 61, 89, 149, 151, 179, 181, 211, 239, 241, 269, 271, 331, 359, 389, 419, 421, 449, 479, 509, 541, 569, 571, 599, 601, 631, 659, 661, 691, 719, 751, 809, 811, 839, 929, 991, 1019, 1021, 1049, 1051, 1109, 1171, 1201, 1229, 1231

Offset: 1

Omar E. Pol, Aug 15 2007

For every prime p here, the cyclotomic polynomial Phi(15p,x) is flat.

Primes in A175887. [Reinhard Zumkeller, Jan 07 2012]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A001097, A001359, A006512, A039949, A057204, A068228, A087715, A129805, A117223, A010051.

a132240 n = a132240_list !! (n-1)
a132240_list = [x | x <- a175887_list, a010051 x == 1]
-- Reinhard Zumkeller, Jan 07 2012

[ p: p in PrimesUpTo(1300) | p mod 30 in {1, 29} ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[1000]],MemberQ[{1,29},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)
Select[Flatten[#+{1,29}&/@(30Range[0,50])],PrimeQ] (* Harvey P. Dale, Sep 08 2021 *)

A257658 Primes of the form A060735(k) +- 1, where A060735 lists multiples of primorials (A002110) less than the next larger primorial.

Original entry on oeis.org

2, 3, 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, 180179, 180181

Offset: 1

James M. McCanney and Robert G. Wilson v, Jul 26 2015

nonn

After a(9), all terms are congruent to +-1 (mod 30).

More generally, for any primorial P (cf. A002110), all terms >= P-1 are congruent to +/- 1 (mod P).- This sequence is essentially the same as A087715. - M. F. Hasler, Jul 27 2015

			149 & 151 are in the sequence because they are primes +-1 from A060735(12) = 150. A term does not have to be a twin prime; those are found in A087732.

James M. McCanney and Robert G. Wilson v, Table of n, a(n) for n = 1..1013

Cf. A060735, A087732, A002110.

Essentially the same as A087715.

f[n_] := Range[Prime[n + 1] - 1] Times @@ Prime@ Range@ n; Select[ Union@ Flatten@ Join[ Array[f, 6] - 1, Array[f, 7, 0] + 1], PrimeQ@# &]

Primes among the numbers produced from A060735 +/- 1.

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A087714 Primes p = prime(i) such that p(i)# - p(i+1) and p(i)# + p(i+1) are both primes, where p# = A002110.

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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).

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A132240 Primes congruent to {1, 29} mod 30.

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A257658 Primes of the form A060735(k) +- 1, where A060735 lists multiples of primorials (A002110) less than the next larger primorial.

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A087716 Base-2 pseudoprimes (see A001567) of the form jp(i)# - p(k) or jp(i)# + p(k), p(i) and p(k) primes with p(i) < p(k) < p(i+1)^2 and 0 < j < p(i+1).