Conference rusure::math

284.0. "Here's a sequence for ya" by TOOLS::STAN () Fri May 17 1985 21:23

Anyone see a simple pattern to the following sequence?
[perhaps involving primes of the form 4n-1 or sums of squares]

1,4,5,9,12,13,16,17,24,25,28,33,36,37,40,41,49,52,57,60,
61,64,65,72,73,81,84,85,88,96,97,100,101,105,108,112,113,116,121,124,
129,133,136,144,145,148,153,156,161,168,169,172,177,180,181,184,192,193,196,197,
201,204,209,217,220,221,225,228,229,232,240,241,249,256,257,264,265,268,273,276,
280,288,289,292,293,297,301,304,305,312,313,316,324,325,328,336,337,345,348,349,
352,353,361,364,365,369,372,376,385,388,393,396,400,401,408,409,416,420,421,424,
432,433,441,444,445,448,449,456,457,460,465,472,477,480,481,484,485,492,497,504,
508,513,517,520,529,532,537,540,544,545,553,556,561,564,568,576,577,580,581,584,
585,592,593,600,601,609,612,613,616,624,625,628,633,640,641,649,652,660,661,672,
673,676,677,684,685,688,689,696,697,700,705,708,709,716,721,724,729,732,733,737,
744,745,753,756,760,761,768,769,772,773,777,784,785,792,793,796,801,805,808,817,
820,828,840,841,844,849,852,856,864,865,868,869,876,880,881,889,897,900,901,904,
913,916,921,924,925,928,929,936,940,948,949,952,953,961,964,969,976,981,984,985,
996,997...

It was generated as the range of the set {m^2 + n^2 - 2 gcd(m,n) + 1}.