A073661 -id:A073661 - cp's OEIS frontend

A073664 Even numbers which retain their relative position in A073661 (are not disturbed in the rearrangement process).

2, 4, 6, 18, 28, 56, 60, 64, 68, 72, 80, 116, 126, 152, 170, 184, 200, 214, 234, 248, 276, 290, 328, 330, 334, 346, 360, 402, 408, 416, 438, 472, 512, 524, 578, 598, 662, 702, 744, 786, 810, 824, 864, 908, 968, 1008, 1030, 1032, 1052, 1076, 1172, 1182, 1220

Offset: 0

Amarnath Murthy, Aug 10 2002

nonn

Cf. A073661, A073662.

More terms from Hans Havermann, Sep 23 2002

A073662 Rearrangement of even numbers such that a(k)*a(k+1) + 1 is a prime for all k.

Original entry on oeis.org

2, 6, 10, 4, 18, 22, 16, 12, 8, 14, 20, 26, 36, 28, 24, 32, 38, 42, 34, 30, 40, 52, 46, 66, 48, 44, 54, 64, 70, 60, 50, 56, 80, 68, 62, 84, 74, 90, 72, 58, 76, 88, 94, 78, 82, 96, 100, 106, 120, 86, 98, 104, 122, 108, 112, 118, 102, 116, 132, 124, 142, 114, 110, 128, 92

Offset: 1

Amarnath Murthy, Aug 10 2002

nonn

a(1)=2; a(n) is the smallest number not already in the sequence such that a(n)*a(n-1) + 1 is a prime. Some numbers retain their places (that is an even number 2n retains its n-th position), such numbers are in A076023.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A073661, A076023.

Avail:= 2*[$2..110]:
A[1]:= 2:
for n from 2 do
    found:= false:
    for i in Avail do
      if isprime(i*A[n-1]+1) then
        A[n]:= i;
        Avail:= subs(i=NULL,Avail);
        found:= true;
        break
     fi
    od;
    if not found then break fi
od:
seq(A[i],i=1..n-1); # Robert Israel, Jul 16 2018

amax = 200; a[1] = 2; aa = Range[4, amax, 2];
a[n_] := a[n] = For[k = 1, k <= Length[aa], k++, an = aa[[k]]; If[PrimeQ[ a[n - 1] an + 1], aa = Delete[aa, k]; Return[an]]];
DeleteCases[Array[a, Floor[amax/2]], Null] (* Jean-François Alcover, Feb 28 2019 *)

More terms from Hans Havermann, Sep 23 2002

A074368 Rearrangement of odd numbers such that a(k) + a(k+1) + 1 is a prime for all k.

Original entry on oeis.org

1, 3, 7, 5, 11, 17, 13, 9, 19, 21, 15, 25, 27, 31, 29, 23, 35, 37, 33, 39, 43, 45, 51, 49, 47, 41, 55, 53, 59, 67, 63, 73, 57, 69, 61, 65, 71, 77, 79, 83, 89, 91, 75, 81, 85, 87, 93, 97, 95, 101, 109, 113, 115, 107, 103, 119, 121, 105, 117, 111, 99, 123, 127, 129, 133, 135

Offset: 1

Hans Havermann, Sep 23 2002

nonn

Cf. A073661.

A073665 Rearrangement of even numbers such that a(n) + a(n+1) + 1 and a(n)*a(n+1) + 1 are primes for all n.

Original entry on oeis.org

2, 8, 14, 32, 20, 26, 62, 38, 50, 56, 80, 68, 110, 86, 140, 98, 74, 122, 104, 128, 152, 44, 92, 134, 212, 176, 170, 146, 116, 200, 158, 224, 194, 164, 218, 242, 188, 272, 284, 308, 254, 314, 278, 290, 230, 248, 182, 206, 302, 296, 260, 326, 332, 350, 236, 320, 266

Offset: 1

Amarnath Murthy, Aug 10 2002

nonn

Cf. A073661, A073662, A073664.

Corrected and extended by Sascha Kurz, Jan 28 2003

cp's OEIS Frontend

A073664 Even numbers which retain their relative position in A073661 (are not disturbed in the rearrangement process).

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A073662 Rearrangement of even numbers such that a(k)*a(k+1) + 1 is a prime for all k.

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A074368 Rearrangement of odd numbers such that a(k) + a(k+1) + 1 is a prime for all k.

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Author

Keywords

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A073665 Rearrangement of even numbers such that a(n) + a(n+1) + 1 and a(n)*a(n+1) + 1 are primes for all n.

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Author

Keywords

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