A054574 -id:A054574 - cp's OEIS frontend

A054575 Number of iterations to reach new prime in A054574.

4, 2, 2, 2, 3, 2, 2, 2, 2, 2, 5, 2, 10, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 4, 2, 3, 3, 3, 2, 3, 3, 2, 2, 6, 18, 2, 2, 2, 16, 3, 16, 4, 2, 2, 4, 3, 2, 4, 2, 2, 5, 3, 2, 3, 2, 3, 4, 6, 3, 2, 12, 10, 2, 2, 4, 2, 4, 2, 2, 10, 2, 4, 3, 2, 4, 2, 3, 2, 2, 9, 6, 2, 2, 20, 3, 2, 3, 3, 3, 2, 10, 15, 2, 2, 11, 10

Offset: 1

Enoch Haga, Apr 11 2000

			a(5)=3 because beginning at 11, the next prime, 47, is attained in 3 steps.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A054574.

f[n_] := n + Plus @@ Times @@@ FactorInteger@n; a[n_] := Length[NestWhileList[f, (p = Prime[n]), # == p || CompositeQ[#] &]] - 1; Array[a, 100] (* Amiram Eldar, Sep 07 2019 *)

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

Original entry on oeis.org

2, 3, 11, 71, 227, 491, 683, 1103, 1187, 2591, 3923, 4271, 4931, 6737, 7193, 7703, 8093, 8753, 8963, 9173, 9377, 10271, 13043, 13451, 13997, 15233, 15443, 15803, 15887, 17957, 18701, 19961, 20681, 21701, 22031, 22073, 24371, 24473, 24683

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

nonn

p=1, q=2(prime), a=3, b=4, c=5, s=12-+1 primes, ...

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281.

lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[q],AppendTo[lst,q]]],{n,8!}];lst

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A054575 Number of iterations to reach new prime in A054574.

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

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cp's OEIS Frontend

A054575 Number of iterations to reach new prime in A054574.

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Author

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.