The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A299952 The sum a(n) + a(n+1) is a substring of the concatenation of all terms up to a(n+1). Lexicographic first sequence of positive integers without duplicate terms having this property. 2
 1, 10, 99, 11, 80, 19, 61, 30, 31, 49, 12, 2, 4, 5, 3, 6, 7, 15, 9, 13, 17, 14, 8, 16, 20, 25, 23, 22, 26, 27, 18, 34, 28, 21, 24, 29, 32, 35, 36, 44, 37, 43, 38, 33, 41, 39, 42, 40, 51, 45, 46, 47, 52, 57, 53, 56, 54, 55, 63, 59, 50, 60, 58, 64, 66, 65, 74, 48, 62, 68, 71, 77, 72, 67, 78, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that does not lead to a contradiction. This is probably a permutation of the natural numbers (after 10000 terms, the smallest integer not yet present is 9990). LINKS Lars Blomberg, Table of n, a(n) for n = 1..10000 EXAMPLE a(1) + a(2) = 1 + 10 = 11 and “11” is visible in [1,10] a(2) + a(3) = 10 + 99 = 109 and “109” is visible in [10,99] a(3) + a(4) = 99 + 11 = 110 and “110” is visible in [1,10] a(4) + a(5) = 11 + 80 = 91 and “91” is visible in [99,11] a(5) + a(6) = 80 + 19 = 99 and “99” is visible in [99] a(6) + a(7) = 19 + 61 = 80 and “80” is visible in [80] ... MATHEMATICA Nest[Function[a, Append[a, Block[{k = 1, d}, While[Nand[FreeQ[a, k], SequenceCount[Flatten@ IntegerDigits[Append[a, k]], IntegerDigits[a[[-1]] + k]] > 0], k++]; k]]], {1}, 75] (* Michael De Vlieger, Feb 22 2018 *) PROG (PARI) a(n, show=1, a=1, s=a, u=[a], t, m)={for(n=2, n, show&&print1(a", "); for(k=u[1]+1, oo, setsearch(u, k)&&next; m=Mod(a+k, 10^#Str(a+k)); t=s*10^#Str(k)+k; until(k>=t\=10, t==m&&(a=k)&&break(2))); s=s*10^#Str(a)+a; u=setunion(u, [a]); u[2]==u[1]+1&&u=u[^1]); a} \\ M. F. Hasler, Feb 22 2018 CROSSREFS Cf. A300000. For a different constraint on a(n)+a(n+1) (must have a digit '1'), see A299957 and A299970, A299982, ..., A299988, A299969  (nonnegative analog with digit 0, 2, ..., 9), A299971, A299972, ..., A299979 (positive analog with digit 0, 2, ..., 9). Cf. A299980, A299981, A299402, A299403, A298974, A298975, A299996, A299997, A298978, A298979 for the analog using multiplication: a(n)*a(n+1) has a digit 0, resp. 1, ..., resp. 9. Sequence in context: A217634 A007137 A135927 * A278672 A129542 A224752 Adjacent sequences:  A299949 A299950 A299951 * A299953 A299954 A299955 KEYWORD nonn,base AUTHOR Eric Angelini and Lars Blomberg, Feb 22 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 21 11:01 EST 2020. Contains 331105 sequences. (Running on oeis4.)