A356664 Numbers k such that A225205(k) is in A354549.
0, 2, 4, 10, 12, 14, 18, 20, 22, 30, 32, 34, 38, 40, 44, 48, 52, 60, 62, 72, 76, 78, 80, 82, 92, 94, 100, 104, 116, 120, 126, 130, 132, 134, 138, 140, 142, 144, 146, 148, 152, 154, 156, 158, 160, 168, 176, 180, 182, 186, 188, 192, 194, 202, 210, 222, 224, 226, 228, 230, 232
Offset: 1
Keywords
Examples
4 is a term because A225204(4) = 125 and A225205(4) = 159, and floor(125^2*phi) = 159^2.
Links
- Jianing Song, Table of n, a(n) for n = 1..293
Programs
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PARI
print1("0, "); my(cofr=A331692_vector_bits(1000), conv=matrix(2, #cofr)); conv[, 1]=[1, 1]~; conv[, 2]=[4, 3]~; for(n=3, #cofr, conv[, n]=cofr[n]*conv[, n-1]+conv[, n-2]; if(n%2 == 1 && (conv[1, n]^2+1)^2 - (conv[1, n]^2+1)*(conv[2, n]^2) - (conv[2, n]^2)^2 > 0, print1(n-1, ", "))) \\ Here conv[1, n] = A225204(n-1), conv[2, n] = A225205(n-1), n odd implies conv[1, n]/conv[2, n] < sqrt((1+sqrt(5))/2); let A = conv[1, n]^2+1, B = conv[2, n]^2, then A^2 - A*B - B^2 > 0 implies A/B > (1+sqrt(5))/2 \\ Modified by Jianing Song, Aug 28 2022 according to Kevin Ryde's program for A331692
Comments