A113058 - OEIS

A113058

a(1) = a(2) = a(3) = 1; for n>2, a(n+1) = a(n) + a(n-1) + a(n-2) iff a(n) is prime, otherwise a(n+1) = a(n) + 1.

1, 1, 1, 2, 4, 5, 11, 20, 21, 22, 23, 66, 67, 156, 157, 380, 381, 382, 383, 1146, 1147, 1148, 1149, 1150, 1151, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 10368, 10369, 24194, 24195, 24196, 24197, 72588, 72589, 72590, 72591, 72592, 72593, 72594, 72595

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

a(4) = 2 because a(4-1) = 1 is not prime, so a(4) = a(3) + 1 = 2.

a(5) = 4 because a(5-1) = 2 is prime, so a(5) = a(4) + a(3) + a(2) = 2+1+1 = 4.

a(6) = 5 because a(6-1) = 4 is not prime, so a(6) = a(5) + 1 = 4 + 1 = 5.

a(7) = 11 because a(7-1) = 5 is prime, so a(7) = a(6) + a(5) + a(4) = 5+4+2 = 11.

a(8) = 20 because a(8-1) = 11 is prime, so a(8) = a(7)+a(6)+a(5) = 11+5+4 = 20.

MATHEMATICA