A109888 Sequence with properties that a(1)=1, no prime appears in the sequence or the first differences and all other integers exactly once (in sequence or first differences).

1, 9, 15, 25, 39, 51, 55, 75, 91, 112, 130, 152, 176, 202, 230, 260, 287, 319, 352, 386, 422, 460, 495, 535, 579, 621, 666, 712, 760, 810, 862, 916, 965, 1022, 1078, 1136, 1196, 1258, 1322, 1385, 1450, 1516, 1584, 1653, 1725, 1795, 1869, 1945, 2022, 2100

Offset

1,2

Comments

Sequence and first differences are:

1.9.15..25..39..51.55..75..91...

.8.6..10..14..12..4..20..16.. etc.

Links

Table of n, a(n) for n=1..50.

Example

Start with a(1)=1; what can we add to produce a(2)? Not 1 (already used), not 2 or 3 (primes), not 4 (produces 5, which is prime), not 6 (produces 7, which is prime) -- 8 is ok and produces 9 (1+8) which is not prime, so a(2) =9; what can we add to a(2) to produce a(3)? Not 1, 2 or 3 (see above), not 4 (produces 13, which is prime), not 5 (prime) -- 6 is ok and produces 15 (9+6), which is not prime, so a(3)=15; what can we add to a(3) to produce a(4)? Not 1, 2 and 3 (see above), not 4 (produces 19, which is prime), not 5 (prime), not 6 (already used), not 7 (prime), not 8 or 9 (already used) -- 10 is ok and produces 25 (15+10), which is not prime, so a(4)=25; etc.

Crossrefs

Sequence in context: A249730 A342418 A251415 * A193227 A014003 A333788

Adjacent sequences: A109885 A109886 A109887 * A109889 A109890 A109891

Keyword

easy,nonn

Author

Eric Angelini, Aug 31 2005

Extensions

Corrected and extended by Ray Chandler, Sep 02 2005

Status

approved