A375792 -id:A375792 - cp's OEIS frontend

A375793 Numbers m such that 2^m == 2 (mod m-th triangular number).

1, 3, 5, 11, 13, 29, 37, 61, 73, 131, 157, 181, 193, 277, 313, 397, 421, 457, 541, 561, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1289, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1905, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917, 3061, 3217, 3253, 3313, 3389, 3457

Offset: 1

Juri-Stepan Gerasimov, Aug 29 2024

nonn

a(19) = 561 is the first composite term of the sequence.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Supersequence of A216822, A217465, A217466 and A375792.

Cf. A000217, A272934, A289382.

[1] cat [m: m in [2..3500] | Modexp(2, m, m*(m+1) div 2) eq 2];

t:= n-> n*(n+1)/2:
q:= m-> is(2&^m-2 mod t(m)=0):
select(q, [$1..3457])[];  # Alois P. Heinz, Sep 21 2024

Select[Range[3457],Mod[2^#-2,#(#+1)/2 ]==0&] (* James C. McMahon, Sep 23 2024 *)

A375794 Numbers k such that 2^k == 2 (mod ((k - 1)k/2)) and not 2^k == 2 (mod ((k - 1)k)).

Original entry on oeis.org

5, 13, 37, 61, 101, 109, 157, 181, 421, 541, 661, 757, 821, 1093, 1621, 1861, 2029, 2053, 2269, 2341, 2437, 2701, 2917, 3277, 3301, 3613, 4621, 4789, 4861, 5461, 5501, 5581, 6301, 6661, 7309, 8101, 8269, 8581, 8821, 8893, 9829, 9901, 10141, 10261, 10501, 10837, 11701, 12101, 12301

Offset: 1

Juri-Stepan Gerasimov, Aug 29 2024

nonn

a(22) = 2701 is the first composite term of the sequence.

Cf. A069051, A375792.

[k: k in [2..13333] | Modexp(2, k, (k^2-k) div 2) eq 2 and not Modexp(2, k, k^2-k) eq 2];

Select[Range[2,12400], PowerMod[2,#,(#-1)#/2]==2 && !PowerMod[2,#,(#-1)#]==2 &] (* Stefano Spezia, Sep 19 2024 *)

isok(k)={k > 1 && Mod(2, (k-1)*k)^k == 2 + (k-1)*k/2} \\ Andrew Howroyd, Aug 29 2024

cp's OEIS Frontend

A375793 Numbers m such that 2^m == 2 (mod m-th triangular number).

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A375794 Numbers k such that 2^k == 2 (mod ((k - 1)k/2)) and not 2^k == 2 (mod ((k - 1)k)).

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cp's OEIS Frontend

A375793 Numbers m such that 2^m == 2 (mod m-th triangular number).

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Author

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Crossrefs

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Magma

Maple

Mathematica

A375794 Numbers k such that 2^k == 2 (mod ((k - 1)*k/2)) and not 2^k == 2 (mod ((k - 1)*k)).

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Author

Keywords

Comments

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Programs

Magma

Mathematica

PARI

A375794 Numbers k such that 2^k == 2 (mod ((k - 1)k/2)) and not 2^k == 2 (mod ((k - 1)k)).