Search a number
gapful n.  and  undulating n.

First numbers that belong to both sets:

121, 242, 363, 484, 1010, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2020, 2121, 2323, 2424, 2525, 2626, 2727, 2828, 2929, 3030, 3131, 3232, 3434, 3535, 3636, 3737, 3838, 3939, 4040, 4141, 4242, 4343, 4545, 4646, 4747, 4848, 4949, 5050, 5151, 5252, 5353, 5454, 5656, 5757, 5858, 5959, 6060, 6161, 6262, 6363, 6464, 6565, 6767, 6868, 6969, 7070, 7171, 7272, 7373, 7474, 7575, 7676, 7878, 7979, 8080, 8181, 8282, 8383, 8484, 8585, 8686, 8787, 8989, 9090, 9191, 9292, 9393, 9494, 9595, 9696, 9797, 9898, 17171, 23232, 46464, 52525, 69696, 101010, 121212, 131313, 141414, 151515, 161616, 171717, 181818, 191919, 202020, 212121, 232323, 242424, 252525, 262626, 272727, 282828, 292929, 303030, 313131, 323232, 343434, 353535, 363636, 373737, 383838, 393939, 404040, 414141, 424242, 434343, 454545, 464646, 474747, 484848, 494949, 505050, 515151, 525252, 535353, 545454, 565656, 575757, 585858, 595959, 606060, 616161, 626262, 636363, 646464, 656565, 676767, 686868, 696969, 707070, 717171, 727272, 737373, 747474, 757575, 767676, 787878, 797979, 808080, 818181, 828282, 838383, 848484, 858585, 868686, 878787, 898989, 909090, 919191, 929292, 939393, 949494, 959595, 969696, 979797, 989898, 1515151, 3434343, 5353535, 6868686, 7272727, 10101010, 12121212, 13131313, 14141414, 15151515, 16161616, 17171717, 18181818, 19191919, 20202020, 21212121, 23232323, 24242424, 25252525, 26262626, 27272727, 28282828, 29292929, 30303030, 31313131, 32323232, 34343434, 35353535, 36363636, 37373737, 38383838, 39393939, 40404040, 41414141, 42424242, 43434343, 45454545, 46464646, 47474747, 48484848, 49494949, 50505050, 51515151, 52525252, 53535353, 54545454, 56565656, 57575757, 58585858, 59595959, 60606060, 61616161, 62626262, 63636363, 64646464, 65656565, 67676767, 68686868, 69696969, 70707070, 71717171, 72727272, 73737373, 74747474, 75757575, 76767676, 78787878, 79797979, 80808080, 81818181, 82828282, 83838383, 84848484, 85858585, 86868686, 87878787, 89898989, 90909090, 91919191, 92929292, 93939393, 94949494, 95959595, 96969696, 97979797, 98989898, 141414141, 282828282, 595959595, 1010101010, 1212121212, 1313131313, 1414141414, 1515151515, 1616161616, 1717171717, 1818181818, 1919191919, 2020202020, 2121212121, 2323232323, 2424242424, 2525252525, 2626262626, 2727272727, 2828282828, 2929292929, 3030303030, 3131313131.

Some larger examples :