A206329 -id:A206329 - cp's OEIS frontend

A206462 Primes p such that p + nextprime(p) is a squarefree number (A005117).

2, 13, 19, 37, 67, 89, 103, 109, 127, 163, 193, 199, 211, 229, 307, 379, 389, 397, 449, 463, 467, 479, 487, 499, 509, 613, 643, 661, 683, 701, 719, 739, 757, 769, 797, 859, 877, 883, 887, 911, 929, 937, 967, 983, 997, 1009, 1093, 1109, 1163, 1201, 1237, 1279

Offset: 1

Zak Seidov, Feb 07 2012

nonn

			13 + 17 = 30 = A206329(2).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A001043, A001358, A005117, A206329.

a206462 n = a206462_list !! (n-1)
a206462_list = map (a000040 . (+ 1)) $
                   elemIndices 1 $ map a008966 a001043_list
-- Reinhard Zumkeller, Feb 08 2012

Prime[Select[Range[200], Abs[MoebiusMu[Prime[#] + Prime[# + 1]]] == 1 &]] (* Alonso del Arte, Feb 08 2012 *)

a(n) + nextprime(a(n)) = A206329(n).

A008966(A001043(A049084(a(n)))) = 1. [Reinhard Zumkeller, Feb 08 2012]

A207637 Squarefree sums of 3 successive primes.

Original entry on oeis.org

10, 15, 23, 31, 41, 59, 71, 83, 97, 109, 131, 143, 159, 173, 187, 199, 211, 223, 235, 251, 269, 287, 301, 311, 319, 329, 349, 371, 395, 407, 439, 457, 471, 487, 503, 519, 533, 551, 565, 581, 589, 607, 633, 661, 679, 689, 701, 713, 731, 749, 771, 789, 803

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 19 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A206329.

Select[Table[Prime[n] + Prime[n + 1] + Prime[n + 2], {n, 300}], SquareFreeQ]

p=2;q=3;forprime(r=5,1e4,if(issquarefree(t=p+q+r),print1(t", "));p=q;q=r) \\ Charles R Greathouse IV, Jun 14 2013

A206626 Primes p such that p + previousprime(p) is a squarefree number.

Original entry on oeis.org

3, 17, 23, 41, 71, 97, 107, 113, 131, 167, 197, 211, 223, 233, 311, 383, 397, 401, 457, 467, 479, 487, 491, 503, 521, 617, 647, 673, 691, 709, 727, 743, 761, 773, 809, 863, 881, 887, 907, 919, 937, 941, 971, 991, 1009, 1013, 1097, 1117, 1171, 1213, 1249, 1283

Offset: 1

Zak Seidov, Feb 10 2012

nonn

			3+2 = 5 = A206462(1), 17+13 = 30 = A206462(2).

Cf. A001043, A001358, A005117, A206329, A206462.

Select[Prime[Range[250]],SquareFreeQ[#+NextPrime[#,-1]]&] (* Harvey P. Dale, Sep 21 2023 *)

a(n) = A206329(n) - A206462 (n).

cp's OEIS Frontend

A206462 Primes p such that p + nextprime(p) is a squarefree number (A005117).

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A207637 Squarefree sums of 3 successive primes.

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A206626 Primes p such that p + previousprime(p) is a squarefree number.

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