A226930 Second differences give the sequence itself, but read digit-by-digit.

1, 2, 4, 8, 16, 32, 49, 72, 98, 126, 158, 199, 247, 297, 356, 423, 491, 561, 637, 714, 796, 886, 977, 1077, 1186, 1297, 1412, 1534, 1658, 1791, 1931, 2074, 2222, 2376, 2534, 2694, 2857, 3024, 3200, 3377, 3559, 3747, 3936

Offset

1,2

Comments

There are many sequences with this property, but this is the lexicographically earliest such sequence which has positive terms and is strictly increasing. For a discussion of the growth rate, see A227844. - N. J. A. Sloane, Aug 20 2013

Links

Alois P. Heinz and N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Example

The second differences are 1, 2, 4, 8, 1, 6, 3, 2, 4, 9, 7, 2, 9, 8, 1, 2, 6, 1, 5, 8, 1, 9, 9, 2, 4, 7, ...

Maple

a:=[1, 2, 4]; b:=[1, 2]; c:=[1]; la:=3; lb:=2; lc:=1;
M:=100;
p:=2;
for n from 1 to M do
N:=a[p];
s:=convert(N, base, 10);
ls:=nops(s);
for i from 1 to ls do
c:=[op(c), s[ls-i+1]]; lc:=lc+1;
b:=[op(b), b[lb]+c[lc]]; lb:=lb+1;
a:=[op(a), a[la]+b[lb]]; la:=la+1;
                   od:
p:=p+1;
od:
[seq(a[i], i=1..la)];
# N. J. A. Sloane, Aug 21 2013

Prog

(Haskell)
digits = map (fromIntegral.digitToInt). show
inverseDiff xs = scanl (+) (head xs) xs
seqA = iterate ((!!2). iterate inverseDiff. concatMap digits) [1]
-- Example (executed in GHCi):
-- > seqA !!4
-- [1, 2, 4, 8, 16, 32, 49, 72, 98, 126, 158, 199, 247, 297]
-- Arie Groeneveld, Aug 31 2013

Crossrefs

Cf. A227844.

Sequence in context: A326079 A222193 A217833 * A326751 A297702 A306314

Adjacent sequences: A226927 A226928 A226929 * A226931 A226932 A226933

Keyword

nonn,base

Author

Eric Angelini, Jul 30 2013

Extensions

More terms from Paolo P. Lava, Jul 30 2013

Status

approved