A257946 a(n) is the least number such that the sum of the products of all pairs of consecutive digits is equal to n.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 25, 219, 26, 419, 27, 35, 28, 819, 29, 1128, 45, 37, 229, 1235, 38, 55, 429, 39, 47, 1146, 56, 1139, 48, 239, 829, 57, 49, 1148, 1247, 439, 58, 1149, 67, 1166, 249, 59, 1158, 1257, 68, 77, 159, 839, 449, 1357, 69, 259, 78, 1177, 1276

Offset

0,1

Links

Paolo P. Lava and Giovanni Resta, Table of n, a(n) for n = 0..10000 (first 500 terms from Paolo P. Lava)

Example

The sum of the products of pairs of consecutive digits of 25 is 2*5 = 10 and 25 is the least number with this property, so a(10) = 25.
The sum of the products of pairs of consecutive digits of 219 is 2*1 + 1*9 = 11. Again, 219 is the least number with this property, so a(11) = 219.

Maple

P:=proc(q) local a, b, c, k, j, n; print(10);
for j from 1 to q do for n from 1 to q do a:=n; b:=[];
for k from 1 to ilog10(n)+1 do b:=[(a mod 10), op(b)];
a:=trunc(a/10); od; a:=add(b[k]*b[k+1], k=1..nops(b)-1);
if a=j then print(n); break; fi; od; od; end: P(10^6);

Mathematica

Join[{10}, With[{tbl=Table[{n, Total[Times@@@Partition[ IntegerDigits[ n], 2, 1]]}, {n, 1400}]}, Flatten[Table[Select[tbl, #[[2]]==k&, 1], {k, 60}], 1]][[All, 1]]] (* Harvey P. Dale, Jun 15 2017 *)

Prog

(PARI) a(n)=k=10; while(sum(i=1, #digits(k)-1, digits(k)[i]*digits(k)[i+1])!=n, k++); k
vector(50, n, n--; a(n)) \\ Derek Orr, May 19 2015

Crossrefs

Sequence in context: A248499 A008716 A011531 * A070839 A161561 A307560

Adjacent sequences: A257943 A257944 A257945 * A257947 A257948 A257949

Keyword

nonn,base

Author

Paolo P. Lava, May 14 2015

Status

approved