A382035 a(n) is the smallest prime q such that q + prime(n) is of form 10^k or 2*10^k, or 0 if no such prime exists.

0, 7, 5, 3, 89, 7, 3, 181, 977, 71, 1999969, 163, 59, 157, 53, 47, 41, 139, 1933, 29, 127, 199921, 17, 11, 3, 999999999899, 97, 999999893, 19891, 887, 73, 9999999999999999999869, 863, 61, 9851, 1999999999849, 43, 37, 9833, 827, 821, 19, 809, 7, 3, 1801, 1789

Offset: 1

Author

Steven Lu, Mar 12 2025

Keywords

• nonn

Comments

a(1) is not the only term equal to 0.

For example, a(37145)=0, since prime(37145)=442609, and:

10^k - 442609 is a multiple of 3, for k>=6,

2*10^(2*k) - 442609 is a multiple of 11, for k>=3,

2*10^(6*k+1) - 442609 is a multiple of 7, for k>=1,

2*10^(6*k+3) - 442609 is a multiple of 13, for k>=1,

2*10^(6*k+5) - 442609 is a multiple of 37, for k>=1.

Examples

			For n=11 (prime(n)=31):
For all positive integer k, 10^k-31 is multiple of 3.
200 - 31 = 169 = 13 * 13
2000 - 31 = 1969 = 11 * 179
20000 - 31 = 19969 = 19 * 1051
200000 - 31 = 199969 = 7 * 7 * 7 * 11 * 53
2000000 - 31 = 1999969 is a prime number.
thus a(11) = 1999969.
		

Crossrefs

Cf. A191474 (base 2 version of this sequence).

Programs

Mathematica

Table[If[MissingQ[#], 0, # - Prime[i]] &@SelectFirst[Flatten[Table[{10^j, 2 10^j}, {j, 100}]], # > Prime[i] && PrimeQ[# - Prime[i]] &], {i, 1, 47}]