A307129 -id:A307129 - cp's OEIS frontend

A307130 Sequence associated to A307129. The terms of the sequence are the successive sums of the successive pairs of adjacent terms of A307129.

30, 50, 70, 72, 50, 52, 70, 92, 90, 301, 270, 30, 32, 30, 50, 70, 74, 70, 90, 181, 210, 301, 270, 181, 210, 301, 270, 181, 210, 301, 270, 181, 210, 3010, 3018, 301, 290, 1092, 1090, 1092, 1090, 1092, 1090, 1290, 3030, 3050, 3052, 3030, 3032, 3030, 3032, 3030, 3050, 3070, 3090, 3092, 3070, 3072, 3070, 3090, 5070, 5072, 3090, 3250, 3030, 3050, 3052, 3030, 3032, 3030, 3032, 3030, 3050, 3070, 3090, 3092, 3070, 3072, 3070, 3090, 5070, 5072, 3090, 5050, 5070, 5090, 5092, 5070, 5072, 5070, 5090, 5292, 5070, 5072, 5070, 5090, 5490, 5070, 5072

Offset: 1

Eric Angelini and Lars Blomberg, Mar 26 2019

The digits of this sequence follow the pattern odd/even/odd/even... as do the digits of the sequence A307129.

A307129 and this sequence need a lot of backtracking to be computed; this means that the last few terms of A307129 and of this sequence might evolve. However, the first 100 terms proposed here seem accurate.

Cf. A307129.

A098951 Smallest available integer fitting the even/odd/even/odd/even... digit pattern (across adjacent numbers).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 210, 10, 12, 14, 16, 18, 30, 32, 34, 36, 38, 50, 52, 54, 56, 58, 70, 72, 74, 76, 78, 90, 92, 94, 96, 98, 101, 212, 103, 214, 105, 216, 107, 218, 109

Offset: 1

Eric Angelini, Oct 21 2004

Different from A097962.

Indeed, A097962 is required to be increasing. Therefore, a(31) = 210 can here be followed by a(32) = 10, while A097962(32) = 301. - M. F. Hasler, Mar 23 2019

			After a(30) = 89, a(31) must start with an even digit. A number consisting of one even digit would work, but they are all in the sequence already. A 2-digit number with first digit even and second digit odd would work, but they are also all in the sequence already. A 3-digit number would have to have even, odd, and even digits in that order. The smallest such number is 210, so a(31) = 210. - _Michael B. Porter_, Mar 25 2019

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A030141, A097962, A307129.

See also A377919.

altQ[n_] := n < 10 || Union[Total /@ Partition[ Mod[ IntegerDigits@n, 2], 2, 1]] == {1}; s = {0}; Do[j=1; While[ MemberQ[s, j] || EvenQ[s[[-1]] + First@ IntegerDigits@ j] || ! altQ[j], j++];  AppendTo[s, j], {68}]; s (* Giovanni Resta, Mar 05 2014 *)
(* longer, but faster *) eoQ[n_] := Module[{d = IntegerDigits[n], alt, i}, alt = Table[If[OddQ[i], -1, 1], {i, d}]; i = 1; While[i++; i <= Length[d] && alt[[i]] == alt[[1]]*(-1)^(i + 1)]; If[i <= Length[d], alt[[1]] = 0]; alt[[1]]]; nn = 10000; tev = {}; tod = {}; Do[If[eoQ[i] == -1, AppendTo[tod, i], If[eoQ[i] == 1, AppendTo[tev, i]]], {i, nn}]; t = {0}; While[tev != {} && tod != {}, If[OddQ[t[[-1]]], AppendTo[t, tev[[1]]]; tev = Rest[tev], AppendTo[t, tod[[1]]]; tod = Rest[tod]]]; t (* T. D. Noe, Mar 05 2014 *)

cp's OEIS Frontend

A307130 Sequence associated to A307129. The terms of the sequence are the successive sums of the successive pairs of adjacent terms of A307129.

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A098951 Smallest available integer fitting the even/odd/even/odd/even... digit pattern (across adjacent numbers).

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