A128994 First of three consecutive pairwise coprime numbers such that the product of any two plus the third is a prime.

1, 2, 3, 5, 6, 8, 19, 25, 32, 38, 53, 84, 110, 114, 119, 122, 125, 129, 133, 159, 170, 175, 229, 235, 263, 302, 313, 320, 385, 419, 489, 495, 543, 572, 593, 643, 749, 786, 815, 866, 929, 949, 966, 1122, 1123, 1173, 1254, 1365, 1459, 1470, 1508, 1542, 1565, 1584

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Example

For 6 the next two numbers such that all are pairwise coprime are 7 and 11.
All three numbers 6*7+11, 6*11+7, 7*11+6 are prime, therefore 6 is in the sequence.

Mathematica

l = {}; For[n = 1, n < 2000, n++, a = n; i = 1; While[Not[GCD[a, a + i]], i++ ]; b = a + i; i = 1; While[Not[GCD[a, b + i] == 1 && GCD[b, b + i] == 1], i++ ]; c = b + i; If[PrimeQ[a*b + c] && PrimeQ[a*c + b] && PrimeQ[b*c + a], AppendTo[l, n]]]; l
apQ[{a_, b_, c_}]:=AllTrue[{a*b+c, b*c+a, a*c+b}, PrimeQ]; tccn[n_]:=
Join[ {n},  Take[Select[Range[n + 1, 20 + n], CoprimeQ[n, #] &], 2]]; Transpose[Select[Table[tccn[n], {n, 1600}], apQ]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 18 2015 *)

Crossrefs

Sequence in context: A088485 A194626 A275323 * A098211 A349792 A218013

Adjacent sequences: A128991 A128992 A128993 * A128995 A128996 A128997

Keyword

nonn

Author

J. M. Bergot, Apr 30 2007

Extensions

Edited and extended by Stefan Steinerberger, Aug 07 2007

Status

approved