A345056 a(n) is the next larger number k > n for which A011772(k) = A011772(n), or n itself if no such larger number exists.

1, 6, 3, 14, 10, 6, 21, 20, 12, 10, 55, 18, 26, 28, 15, 62, 34, 36, 57, 24, 21, 33, 253, 30, 50, 39, 117, 28, 58, 40, 93, 72, 66, 68, 105, 36, 74, 95, 78, 60, 82, 70, 129, 48, 45, 69, 1081, 88, 56, 75, 153, 130, 106, 63, 55, 84, 171, 203, 1711, 120, 122, 124, 126, 254, 325, 66, 201, 136, 92, 210, 355, 96, 146, 111, 100, 114

Offset: 1

Author

Antti Karttunen, Jun 07 2021

Keywords

• nonn

Crossrefs

Cf. A000217, A002024, A011772, A066561, A345057, A345058.

Programs

PARI

A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
A345056(n) = { my(x=A011772(n), y=binomial(x+1,2)); for(i=1+n,y,if(A011772(i)==x,return(i))); (n); };

Formula

a(n) = n + A345057(n).