A088072 Numbers sandwiched between two numbers having only one prime divisor (at least) one of which is composite.

3, 8, 10, 24, 26, 28, 48, 80, 82, 126, 168, 242, 360, 728, 840, 1368, 1848, 2208, 2400, 3720, 5040, 6562, 6858, 7920, 10608, 11448, 14640, 16128, 17160, 19320, 19682, 24390, 28560, 29790, 29928, 36480, 44520, 49728, 50652, 54288, 57120, 59050

Offset

1,1

Comments

Terms of A088071 which are not terms of A014574 (average of twin prime pairs).

Conjecture (1): Sequence is infinite. Conjecture (2): There are only finitely many terms which are sandwiched between composite numbers (26 is the only such term below 1000000).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

8 is a term since 7 is prime and 9 = 3*3 is composite; 26 is a term since 25 = 5*5 and 27 = 3*3*3 are both composite.

Prog

(PARI) {for(n=2, 60000, if(matsize(factor(n-1))[1]*matsize(factor(n+1))[1]==1&&factor(n-1)[1, 2]*factor(n+1)[1, 2]>1, print1(n, ", ")))}

Crossrefs

Cf. A088071, A014574.

Sequence in context: A373200 A332976 A032914 * A213033 A305176 A046545

Adjacent sequences: A088069 A088070 A088071 * A088073 A088074 A088075

Keyword

nonn

Author

Amarnath Murthy, Sep 22 2003

Extensions

Edited and extended by Klaus Brockhaus, Sep 25 2003

Status

approved