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A008321

Smallest number that is not the sum of squares of distinct earlier terms.

1, 2, 3, 6, 7, 8, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 38, 39, 42, 43, 44, 47, 48, 51, 52, 55, 56, 57, 60, 61, 66, 67, 70, 71, 72, 75, 76, 79, 80, 81, 82, 83, 84, 87, 88, 91, 92, 93, 96, 97, 102, 103, 106, 107, 108, 111, 112, 115

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OFFSET

1,2

COMMENTS

There is an isolated large gap between a(166) = 516 and a(167) = 6599859.

a(n) = n + 6600044 on the precise range 332 <= n <= 43558132219836.

REFERENCES

Mihaly Bencze [Beneze], Smarandache Recurrence Type Sequences, Bull. Pure Appl. Sciences, Vol. 16E, No. 2 (1997), pp. 231-236.

F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House, 2000.

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.

LINKS

David W. Wilson, Table of n, a(n) for n = 1..10000

F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.

Eric Weisstein's World of Mathematics, Smarandache Sequences.

EXAMPLE

59 is not in the sequence because it is a sum of squares of terms smaller than 59: 1^2 + 3^2 + 7^2.

PROG

(PARI) {A008321_upto(N)=my(S=1, n=0); vector(N, i, while(bittest(S, n++), ); S=bitor(S, S<<n^2); n)} \\ M. F. Hasler, Jul 07 2025

CROSSREFS

Cf. A000290, A004431 (sums of 2 distinct squares).