By N. J. A. Sloane

ISBN-10: 012648550X

ISBN-13: 9780126485509

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**Extra resources for A Handbook of Integer Sequences**

**Sample text**

Withgf 00 1 + x + x2 + 2x3 + 2x4 + · · · = Π ( 1 + *')■ i= l The partitions of the even numbers into parts which are powers of two form the binary partition function b(n), seq. 378: 1, 2, 4, 6, 10, 14, 20, 26, 36, 46, . , with recurrence b{n) = b(n- 1) + b([in]). P(D = l 1 p(2) = 2 2, l 2 p(3) = 3 3, 21, l 3 p(4) = 5 4, 31, 2 2 , 21 2 , l 4 p(5) = 7 5 , 4 1 , 32, 31 2 , 2 2 1, 21 3 , l 5 p(6) = 11 6, 51, 42, 41 2 , 3 2 , 321, 31 3 , 23, 2 2 1 2 , 21 4 , l 6 p{l) 7, 61, 52, 51 2 , 43, 421, 41 3 , 3 2 1, 322, 321 2 , 31 4 , 2 3 1, 2 2 1 3 , 21 5 , l 7 = 15 Fig.

HS1. CM1 134. 36 1, 2, 1, 2, 2, 1, 2, 1,2, 2, 1,2, 2, 1,2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1,2, 1, 2, 2, 1,2, 1,2,2, 1,2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1,2,2, 1,2, 1,2, 2, 1,2, 2, 1 A SELF-GENERATING SEQUENCE. REF AMM 64 198 57. 37 1,2, 1,2,2, 1 , 3 , 2 , 2 , 3 , 1 , 3 , 3 , 2 , 4 , 2 , 3 , 3 , 1 , 4 , 3 , 3 , 5 , 2 , 4 , 4 , 2 , 5 , 3 , 3 , 4 , 4, 3, 6, 3, 5, 5, 2, 6, 4, 4, 6, 2, 5, 5, 3, 6, 3, 4, 4, 1, 5 REPRESENTATIONS AS A SUM OF FIBONACCI NUMBERS. REF FQ 4 305 66.

108 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 6, 6, 4, 6, 6, 2, 10, 2, 4, 2, 12, 12, 4, 2, 4, 6, 2, 10, 6, 6, 6, 2, 6, 4, 2, 10, 14, 4, 2, 4 DIFFERENCES BETWEEN CONSECUTIVE PRIMES. REF AS1 870. 40 1,2,2,4,7, 12, 16,32, ... 124 109 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32 RELATED TO BINARY EXPANSION OF N.

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