A341013 The cumulative sum of the prime digits so far in the sequence and the cumulative sum of the nonprime digits so far differ by n for all a(n) values.

1, 3, 12, 16, 10, 34, 43, 56, 65, 78, 87, 100, 236, 258, 263, 285, 304, 326, 340, 359, 362, 395, 403, 430, 447, 474, 506, 528, 539, 560, 582, 593, 605, 623, 632, 650, 708, 744, 780, 807, 825, 852, 870, 935, 953, 1000, 1112, 1121, 1145, 1154, 1167, 1176

Offset

1,2

Comments

The prime digits are 2, 3, 5 and 7; the nonprime digits are 0, 1, 4, 6, 8 and 9.

This is the lexicographically earliest sequence of distinct integers > 0 having this property.

Links

Carole Dubois, Table of n, a(n) for n = 1..5000

Example

Say that the current sequence is S, the cumulative sum at any moment of the prime digits of S is P, the cumulative sum at any moment of the nonprime digits of S is N and the absolute difference |P-N| is D. We would then have:
S =  1, 3, 12, 16, 10, 34, 43, 56, 65, 78, 87, 100,...
P =  0  3   5   5   5   8  11  16  21  28  35   35
N =  1  1   2   9  10  14  18  24  30  38  46   47
D =  1  2   3   4   5   6   7   8   9  10  11   12 <-- this is = n

Crossrefs

Cf. A085562, A085563.

Cf. A341012 (the cumulative sums of even vs odd digits differ by n).

Sequence in context: A013191 A332959 A009783 * A192786 A277738 A064106

Adjacent sequences: A341010 A341011 A341012 * A341014 A341015 A341016

Keyword

base,nonn

Author

Carole Dubois and Eric Angelini, Feb 02 2021

Status

approved