A330129 a(n) is the last term of the analogous sequence to A121805, but with initial term n, or -1 if that sequence is infinite.

99999945, 9999999999999918, 36, 9999945, 999945, 9999999999999999936, 936, 9999999999972, 999999936, 999936, 999936, 99999945, 999954, 999918, 72, 99999918, 999999999927, 18, 999981, 999999999999999963, 99981, 999999999999999963, 999936, 9999999999999918, 9963

Offset

1,1

Comments

The numbers of terms of the corresponding sequences are in A330128.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube

Mathematica

nxt[x_] := Block[{p=1, n=x}, While[n >= 10, n = Floor[n/10]; p *= 10]; p (n + 1)]; a[n_] := Block[{nT=1, nX=n, w1, w2, w3, x, it, stp, oX}, stp = 100; w1 = w2 = w3 = 0; While[True, oX = nX; nT++; x = 10*Mod[oX, 10]; nX = SelectFirst[Range[9], IntegerDigits[oX + x + #][[1]] == # &, 0]; If[nX == 0, Break[], nX = nX + oX + x]; If[nT == stp, stp += 100; w1=w2; w2=w3; w3=nX; If[w3 + w1 == 2 w2 && Mod[w3 - w2, 100] == 0, it = Floor[(nxt[nX] - nX - 1)/(w3 - w2)]; nT += it*100; nX += (w3 - w2)*it; w3=nX; stp += it*100]]]; oX]; Array[a, 30]

Prog

(Python)
def nxt(x):
    p, n = 1, x
    while n >= 10:
        n //= 10
        p *= 10
    return p * (n + 1)
def a(n):
    nT, nX, w1, w2, w3, stp  = 1, n, 0, 0, 0, 100
    while True:
        oX = nX
        nT += 1
        x = 10*(oX%10)
        nX = next((y for y in range(1, 10) if str(oX+x+y)[0] == str(y)), 0)
        if nX == 0: break
        else: nX += oX + x
        if nT == stp:
            stp += 100
            w1, w2, w3 = w2, w3, nX
            if w3 + w1 == 2*w2 and (w3 - w2)%100 == 0:
                it = (nxt(nX) - nX - 1)//(w3 - w2)
                nT += it*100
                nX += (w3 - w2)*it
                w3 = nX
                stp += it*100
    return oX
print([a(n) for n in range(1, 30)]) # Michael S. Branicky, Nov 18 2023 after Giovanni Resta

Crossrefs

Cf. A330128, A121805, A139284, A366492.

Sequence in context: A251357 A168640 A202722 * A182750 A033424 A017180

Adjacent sequences: A330126 A330127 A330128 * A330130 A330131 A330132

Keyword

nonn,base

Author

Giovanni Resta, Dec 02 2019

Extensions

Escape clause added to definition by N. J. A. Sloane, Nov 14 2023

Status

approved