A171928 -id:A171928 - cp's OEIS frontend

A241977 Numbers k>1 such that 10^phi(k) == 1 (mod k^2), where phi(n)=A000010(n).

3, 487, 1461, 4383, 13149, 39447, 118341, 355023, 56598313, 169794939, 509384817, 1754547703, 5263643109, 7187985751, 15790929327, 21563957253, 27563378431, 33902389487, 47372787981, 50315900257, 64691871759, 82690135293, 101707168461, 150947700771

Offset: 1

Felix Fröhlich, Aug 10 2014

nonn

Giovanni Resta, Table of n, a(n) for n = 1..130 (terms < 10^15)

Cf. A000010, A045616, A077816, A171928, A242958, A242959, A242960, A245529.

Select[Range[400000], PowerMod[10, EulerPhi[#], #^2] == 1 &] (* Amiram Eldar, Oct 16 2023 *)

for(n=2, 1e9, if(Mod(10, n^2)^(eulerphi(n))==1, print1(n, ", ")))

Terms a(12) and beyond from Giovanni Resta, Jan 24 2020

A171926 Position where A171921(n) first occurs in A171922.

Original entry on oeis.org

1, 2, 4, 7, 10, 15, 17, 20, 23, 25, 26, 31, 37, 39, 40, 41, 42, 44, 50, 53, 56, 59, 60, 71, 73, 81, 86, 92, 97, 104, 105, 111, 115, 116, 118, 120, 126, 131, 139, 141, 142, 143, 153, 164, 166, 169, 177, 180, 181, 191, 193, 195, 196, 198, 203, 205, 206, 208, 212, 225, 230, 232

Offset: 1

Hugo van der Sanden, Oct 23 2010

nonn

Hugo van der Sanden, Table of n, a(n) for n = 1..2347

Cf. A171921, A171922, A171927, A171928.

A179267 Numbers n which divide the periodic part (with zeros at end) of the decimal expansion of 1/n.

Original entry on oeis.org

3, 6, 487, 974, 1461, 2435, 2922, 4383, 4870, 7305, 8766, 12175, 13149, 14610, 17532, 21915, 24350, 26298, 29220, 36525, 43830, 48700, 52596, 65745, 73050, 87660, 109575, 131490, 146100, 219150, 262980, 328725, 438300, 657450, 1095750

Offset: 1

T. D. Noe, Jul 06 2010

There are two definitions of the periodic part: zeros may either begin or end the periodic part. For example, for 1/11 = 0.0909090..., the periodic part could be either 09 or 90. This sequences assumes that the zeros are at the end of the periodic part. See A171928 for the case of zeros at the beginning of the periodic part.

Note that the terms following 487 are divisible by 487. This pattern continues until the prime number 56598313, which is another member of A045616.

Reap[Do[k=RealDigits[1/n][[1,-1]]; If[Head[k] === List && Mod[FromDigits[k],n] == 0, Sow[n]], {n,10000}]][[2,1]]

cp's OEIS Frontend

A241977 Numbers k>1 such that 10^phi(k) == 1 (mod k^2), where phi(n)=A000010(n).

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A171926 Position where A171921(n) first occurs in A171922.

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A179267 Numbers n which divide the periodic part (with zeros at end) of the decimal expansion of 1/n.

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Programs

Mathematica