A228589 Starting from a(1)=1, a(n) is the minimum integer greater than a(n-1) such that a(n)+a(n-1) and a(n)*a(n-1)-1 are both primes.

1, 4, 15, 16, 27, 32, 57, 70, 81, 92, 147, 164, 183, 200, 231, 232, 255, 266, 327, 356, 387, 400, 423, 430, 561, 562, 567, 584, 645, 716, 717, 764, 807, 812, 855, 866, 1005, 1006, 1083, 1138, 1203, 1208, 1233, 1298, 1359, 1372, 1395, 1396, 1455, 1498, 1551, 1568

Offset

1,2

Comments

Terms are alternately odd and even.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

a(5)=27 and 27+28=55, 27+29=56, 27+30=57, 27+31=58 are not prime but 27+32=59 is prime and also 27*32-1=863. Thus a(6)=32.

Maple

with(numtheory); P:=proc(q) local a, b, n; a:=1; b:=0; print(a);
for n from 1 to q do while not isprime(a+b) and not isprime (a*b-1) do
b:=b+2; od; print(b); a:=b; b:=b+1; od; print(); end: P(10^4);

Crossrefs

Cf. A228588, A228590.

Sequence in context: A152442 A161769 A135658 * A066862 A228590 A103540

Adjacent sequences: A228586 A228587 A228588 * A228590 A228591 A228592

Keyword

nonn

Author

Paolo P. Lava, Aug 27 2013

Status

approved