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proposed

Numbers n such that when the n-th Catalan restricted growth string [b_k, b_{k-1}, ..., b_2, b_1] as represented by (see A239903(n) is viewed as a simple numeral in Catalan Base: b_k*C(k) + b_{k-1}*C(k-1) + ... + b_2*C(2) +b_1*C(1) it differs from n. Here C(m) = A000108(m).

Numbers n such that when an underlying the Catalan restricted growth string [b_k, b_{k-1}, ..., b_2, b_1] as represented by A239903(n) is viewed as a simple numeral in Catalan Base: b_k*C(k) + b_{k-1}*C(k-1) + ... + b_2*C(2) +b_1*C(1) it differs from n. Here C(m) = A000108(m).

Complement: of A244155. Positions of nonzeros in A244157.

Antti Karttunen, <a href="/A244156/b244156.txt">Table of n, a(n) for n = 1..16156</a>

Numbers k n such that when an underlying restricted growth string [b_k, b_{k-1}, ..., b_2, b_1] as represented by A239903(kn) when is viewed as a simple numeral in Catalan Base: b_k*C(k) + b_{k-1}*C(k-1) + ... is different + b_2*C(2) +b_1*C(1) it differs from kn. Here C(m) = A000108(m).

allocated for Antti KarttunenNumbers k such that A239903(k) when viewed as a simple .. is different from k.

10, 11, 12, 13, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 52, 53, 54, 55, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105

1,1

(Scheme, with Antti Karttunen's IntSeq-library)

(define A244156 (MATCHING-POS 1 1 (lambda (k) (not (= k (CatBaseSum (A239903raw k))))))) ;; A239903raw given in A239903.

(define (CatBaseSum lista) (let loop ((digits (reverse lista)) (i 1) (s 0)) (if (null? digits) s (loop (cdr digits) (+ i 1) (+ s (* (car digits) (A000108 i)))))))

Complement: A244155.

Cf. A000108, A239903, A014418.

allocated

nonn

Antti Karttunen, Jun 22 2014

approved

editing

allocated for Antti Karttunen

allocated

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