A385241 a(n) is the least positive integer k such that the digit sum of prime(n) + k divides the concatenation of prime(n) - 1 and prime(n), where prime(n) is the n-th prime.

1, 7, 4, 3, 1, 87, 4, 70, 4, 1, 3, 63, 4, 57, 53, 36, 2, 4, 33, 29, 27, 21, 9, 11, 3, 1, 897, 4, 891, 4, 873, 4, 64, 861, 4, 849, 843, 16, 4, 28, 22, 819, 10, 807, 4, 801, 789, 777, 73, 370, 67, 4, 759, 49, 4, 37, 31, 729, 723, 19, 6, 7, 693, 4, 687, 683, 669, 663, 4, 651, 647, 20, 1

Offset

1,2

Comments

The scatterplot shows an interesting pattern where many terms lie on one decreasing straight line below which the remaining terms are distributed more randomly although some are also aligned.

Links

Table of n, a(n) for n=1..73.

Example

For n = 1, 1 is the least integer such that 3 which is the digit sum of prime(1) + 1 = 2 + 1 = 3 divides the concatenation of prime(1) - 1 and prime(1) = 12 since 12/3 = 4.
For n = 5, 1 is the least integer such that 3 which is the digit sum of prime(5) + 1 = 11 + 1 = 12 divides the concatenation of prime(5) - 1 and prime(5) = 1011 since 1011/3 = 337.
For n = 8 , 70 is the least integer such that 17 which is the digit sum of prime(8) + 70 = 19 + 70 = 89 divides the concatenation of prime(8) -1 and prime(8) = 1819 since 1819/17 = 107.

Mathematica

a[n_]:=Module[{k=0}, Until[Divisible[FromDigits[Join[IntegerDigits[Prime[n]-1], IntegerDigits[Prime[n]]]], DigitSum[Prime[n]+k]], k++]; k]; Array[a, 73] (* James C. McMahon, Aug 04 2025 *)

Prog

(PARI) a(n) = my(c=fromdigits(concat(digits(prime(n)-1), digits(prime(n)))), k=1); while(c%sumdigits(prime(n)+k), k++); k;

Crossrefs

Cf. A000040, A007953.

Cf. A385172.

Sequence in context: A200121 A198348 A019857 * A363093 A296474 A194705

Adjacent sequences: A385238 A385239 A385240 * A385242 A385243 A385244

Keyword

nonn,easy,base

Author

Claude H. R. Dequatre, Jul 28 2025

Status

approved