[seqfan] Sums in the right place

[Éric Angelini]

[Brussels, spring equinox 2020, 14:07]
Hello SeqFans
In the hereunder sequence S any pair of adjacent terms sums up to a number k visible in position k. This is the lexicographically earliest sequence of distinct positive integers with this property.

S=1,2,3,4,5,6,7,8,9,11,113,15,17,120,12,14,26,10,16,32,18,36,20,40,22,24,46,48,50,23,54,56,19,60,621,13,27,170,37,375,77,79,21,25,29,31,39,34,69,41,59,8100,103,38,35,110,42,28,45,1120,51,240,128,61,320,71,370,141,81,451,30,115,201,560,33,44,66,58,52,68,64,73,47,53,57,43,55,65,91,890,49,75,197,62,83,106,207,63,74,67,70,82,107,90,99,98,109,80,72,84,105,...

Examples (asterisks follow multiple visible solutions) :
1+2=3, 2+3=5, 3+4=7, 4+5=9, 5+6=11, 6+7=13, 7+8=15, 8+9=17, 9+11=20, 11+113=124*, 113+15=128, 15+17=32, 17+120=137*, 120+12=132*, 12+14=26*, 14+26=40*, 26+10=36, 10+16=26*, 16+32=48, 32+18=50, 18+36=54*, 36+20=56, 20+40=60*, 40+22=62, 22+24=46*, 46+48=94, 48+50=98*, 50+23=73*, 23+54=77*, 54+56=110*, 56+19=75, 19+60=79, 60+621=681, 621+13=634, 13+27=40*, 27+170=197*, 170+37=207*, 37+375=412, 375+77=452, 77+79=156*, 79+21=100*, 21+25=46*, 25+29=54*, 29+31=60*, 31+39=70*, 39+34=73*, 34+69=103, 69+41=110*, 41+59=100*.

The same on my personal blog with colors:
http://cinquantesignes.blogspot.com/2020/05/sums-in-right-place.html
Best,
É.