A295149 Numbers n such that gcd(A002487(n), A002487(n+2)) > 1.

5, 11, 23, 33, 45, 47, 49, 61, 73, 85, 95, 105, 117, 153, 163, 165, 187, 191, 195, 217, 219, 229, 257, 259, 269, 271, 273, 283, 285, 313, 325, 339, 353, 363, 365, 367, 369, 381, 383, 385, 397, 399, 401, 403, 413, 427, 441, 453, 481, 483, 493, 495, 497, 507

Offset: 1

Author

Rémy Sigrist, Nov 15 2017

Keywords

• nonn

Comments

All terms are odd (as for any k > 0, gcd(A002487(2*k), A002487(2*k+2)) = gcd(A002487(k), A002487(k+1)) = 1).

This sequence is infinite as it contains A055010(n) for any n > 1.

For any n > 1, gcd(A002487(A055010(n)), A002487(A055010(n)+2)) = 2*n-1.

For any n > 0, gcd(A002487(a(n)), A002487(a(n)+2)) is odd (as A002487(k) is even iff k is divisible by 3).

Crossrefs

Cf. A002487, A055010.

Programs

PARI

fusc(n)=local(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); b \\ after Charles R Greathouse IV at A002487
for (n=1, 507, if (gcd(fusc(n),fusc(n+2))>1, print1 (n", ")))