A129998 Let p < q be consecutive primes. Then p is in the sequence if p+q+p*q is a composite number and if there is a prime number r such that p+q+r is a divisor of p+q+p*q.

31, 37, 61, 67, 71, 97, 103, 107, 127, 139, 149, 157, 179, 191, 193, 197, 199, 227, 239, 263, 269, 271, 277, 281, 293, 313, 337, 353, 359, 367, 379, 397, 401, 433, 461, 463, 487, 491, 499, 541, 563, 571, 599, 601, 607, 619, 631, 653, 661, 719, 733, 751, 757

Offset

1,1

Comments

31 is a prime number; 31+37+31*37 = 1215 = 3^5*5 is composite. The prime number 13 yields, when added to 31+37, the divisor 81. Therefore 31 is in the sequence.

Links

Table of n, a(n) for n=1..53.

Mathematica

a = {}; For[n = 1, n < 200, n++, b = Prime[n] + Prime[n + 1] + Prime[n]*Prime[n + 1]; If[ ! PrimeQ[b], For[i = 1, Prime[i] < Prime[n]*Prime[n + 1], i++, If[Mod[ b, Prime[i] + Prime[n] + Prime[n + 1]] == 0, AppendTo[a, Prime[n]]]]]]; Union[a, a]

Crossrefs

Sequence in context: A291994 A255223 A230225 * A180542 A097437 A156974

Adjacent sequences: A129995 A129996 A129997 * A129999 A130000 A130001

Keyword

nonn,less

Author

J. M. Bergot, Aug 15 2007

Extensions

Edited and extended by Stefan Steinerberger, Nov 22 2007

Status

approved