login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A257946
a(n) is the least number such that the sum of the products of all pairs of consecutive digits is equal to n.
1
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
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, May 14 2015
STATUS
approved