First seven infinite families for 7-digit consecutive palindromes are known, so far. Given a nonnegative integer n, we have the following representations: 1) For each j = 36+12n, k = (816 + 2474*j + 3114*j^2 + 2117*j^3 + 852*j^4 + 209*j^5 + 30*j^6 + 2*j^7)/12 is a term of the sequence in each of three consecutive integer bases: . base 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit ---- --------- --------- --------- --------- --------- --------- --------- j+1 (j+5)/6 (j+11)/2 (5*j+187)/12 22 (5*j+187)/12 (j+11)/2 (j+5)/6 j+2 (j-2)/6 (j+2)/2 (5*j-10)/12 j-2 5*(j-2)/12 (j+2)/2 (j-2)/6 j+3 (j-9)/6 (j+7)/2 (5*j-123)/12 14 (5*j-123)/12 (j+7)/2 (j-9)/6 . First several terms of this form: 19683596522, 133256051308, 597702412638, 2055729074336, 5872897399570, 14629218708372, 32796716348678, 67633053569608, ... 2) For each j = 55+6n, k = (245 + 748 j + 980 j^2 + 718 j^3 + 320 j^4 + 88 j^5 + 14 j^6 + j^7)/6 is a term of the sequence in each of three consecutive integer bases: . base 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit ---- --------- --------- --------- --------- --------- --------- --------- j+1 (j+4)/6 (j+8)/2 (j+52)/6 (j+24)/2 (j+52)/6 (j+8)/2 (j+4)/6 j+2 (j-3)/6 (j+1)/2 (j-3)/6 (j-1)/2 (j-3)/6 (j+1)/2 (j-3)/6 j+3 (j-10)/6 (j+8)/2 (j-58)/6 (j+24)/2 (j-58)/6 (j+8)/2 (j-10)/6 . First several terms of this form: 326217315210, 657158314249, 1242101453540, 2226313335987, 3815123088334, 6290902501325, 10032985497864, 15540762075415, ... 3) For each j = 73+2n, k = (247 + 748 j + 980 j^2 + 718 j^3 + 320 j^4 + 88 j^5 + 14 j^6 + j^7)/2 is a term of the sequence in each of three consecutive integer bases: . base 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit ---- --------- --------- --------- --------- --------- --------- --------- j+1 (j+6)/2 (j+24)/2 (j+54)/2 (j+72)/2 (j+54)/2 (j+24)/2 (j+6)/2 j+2 (j-1)/2 (j+3)/2 (j-1)/2 (j-3)/2 (j-1)/2 (j+3)/2 (j-1)/2 j+3 (j-8)/2 (j+24)/2 (j-56)/2 (j+72)/2 (j-56)/2 (j+24)/2 (j-8)/2 . First several terms of this form: 6678940007962, 8029674745361, 9608108112996, 11445369265003, 13575903004478, 16037727906357, 18872707503976, 22126834861871, ... 4) For each j = 116+12n, k = (2440 + 7366 j + 9694 j^2 + 7171 j^3 + 3232 j^4 + 895 j^5 + 142 j^6 + 10 j^7)/12 is a term of the sequence in each of three consecutive integer bases: . base 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit ---- --------- --------- --------- --------- --------- --------- --------- j+1 (5*j+48)/6 (j+41)/2 (7*j+537)/12 58 (7*j+537)/12 (j+41)/2 (5*j+48)/6 j+2 (5*j-2)/6 (j+4)/2 (7*j-10)/12 j-1 (7*j-10)/12 (j+4)/2 (5*j-2)/6 j+3 (5*j-37)/6 (j+37)/2 (7*j-473)/12 50 (7*j-473)/12 (j+37)/2 (5*j-37)/6 . First several terms of this form: 265965216105640, 523804740539318, 971661769448340, 1714289506887778, 2898325221543488, 4723771969827150, 7457412011740588, 11448302413102970, ... 5) For each j = 172+6n, k = (812 + 2446 j + 3290 j^2 + 2527 j^3 + 1190 j^4 + 343 j^5 + 56 j^6 + 4 j^7)/6 is a term of the sequence in each of three consecutive integer bases: . base 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit ---- --------- --------- --------- --------- --------- --------- --------- j+1 (2*j+14)/3 15 (j+175)/6 36 (j+175)/6 15 (2*j+14)/3 j+2 2*j/3 1 j/6 1 j/6 1 2*j/3 j+3 (2*j-14)/3 15 (j-175)/6 36 (j-175)/6 15 (2*j-14)/3 . First several terms of this form: 3219426999580862, 4081687336404300, 5134773827016778, 6412656227254592, 7953979347481398, 9802529897345332, 12007733429254850, 14625182321158248, ... 6) For each j = 288+12n, k = (1176 + 3566 j + 4374 j^2 + 2807 j^3 + 1032 j^4 + 227 j^5 + 30 j^6 + 2 j^7)/12 is a term of the sequence in each of three consecutive integer bases: . base 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit ---- --------- --------- --------- --------- --------- --------- --------- j+1 (j+5)/6 (j+13)/2 (11*j+277)/12 34 (11*j+277)/12 (j+13)/2 (j+5)/6 j+2 (j-2)/6 (j+4)/2 (11*j-10)/12 n-5 (11*j-10)/12 (j+4)/2 (j-2)/6 j+3 (j-9)/6 (j+9)/2 (11*j-213)/12 26 (11*j-213)/12 (j+9)/2 (j-9)/6 . First several terms of this form: 28854914566144178, 38319170448644248, 50328505820053806, 65429470099944980, 84258744613032682, 107553860268637008, 136164733280322278, 171066049024431436, ... 7) For each j = 277+6n, k = (1237 + 3740 j + 4900 j^2 + 3590 j^3 + 1600 j^4 + 440 j^5 + 70 j^6 + 5 j^7)/6 is a term of the sequence in each of three consecutive integer bases: . base 1st digit 2nd digit 3rd digit 4th digit 5th digit 6th digit 7th digit ---- --------- --------- --------- --------- --------- --------- --------- j+1 (5*j+32)/6 (j+40)/2 (5*j+272)/6 (j+120)/2 (5*j+272)/6 (j+40)/2 (5*j+32)/6 j+2 (5*j-3)/6 (j+5)/2 (5*j-3)/6 (j-5)/2 (5*j-3)/6 (j+5)/2 (5*j-3)/6 j+3 (5*j-38)/6 (j+40)/2 (5*j-278)/6 (j+120)/2 (5*j-278)/6 (j+40)/2 (5*j-38)/6 . First several terms of this form: 109665618707825827, 127278239800098762, 147261829165899797, 169876612631790652, 195405181056545847, 224153902044512702, 256454389857665737, 292665034702086672, ...