A363379 -id:A363379 - cp's OEIS frontend

A180405 Smallest integer not yet present in the sequence such that the sum of the first a(n) terms of the sequence is a prime.

2, 1, 4, 6, 3, 7, 8, 10, 11, 15, 12, 18, 14, 16, 22, 24, 19, 31, 28, 20, 23, 37, 36, 30, 26, 34, 29, 35, 42, 38, 40, 32, 39, 45, 52, 44, 54, 46, 56, 60, 43, 51, 50, 64, 84, 48, 49, 53, 68, 58, 62, 78, 70, 66, 57, 59, 82, 92, 90, 88, 63, 77, 72, 94, 67, 79, 76, 102, 71, 81, 96, 100

Offset: 1

Paolo P. Lava, Sep 02 2010

From an idea of Eric Angelini with additional terms from D. S. McNeil.
The partial sums of the sequence are 2, 3, 7, 13, 16, 23, 31, 41, 52, ...
The sequence is self-descriptive and says that the 2nd, 1st, 4th, 6th, 3rd, 7th, etc, term in the partial sums, namely 3, 2, 13, 23, 7, 31 etc, are primes.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Eric Angelini, The sum of the a(n) first digits of S is a prime
Eric Angelini, The sum of the a(n) first digits of S is a prime [Cached copy, with permission]

Cf. A054408, A171007 (digits version), A363379 (complement).

Examples replaced with a comment by R. J. Mathar, Nov 18 2010

A363450 Partial sums of A180405.

Original entry on oeis.org

2, 3, 7, 13, 16, 23, 31, 41, 52, 67, 79, 97, 111, 127, 149, 173, 192, 223, 251, 271, 294, 331, 367, 397, 423, 457, 486, 521, 563, 601, 641, 673, 712, 757, 809, 853, 907, 953, 1009, 1069, 1112, 1163, 1213, 1277, 1361, 1409, 1458, 1511, 1579, 1637, 1699, 1777, 1847, 1913, 1970

Offset: 1

Neal Gersh Tolunsky, Jun 02 2023

The construction in A180405 means that if n is in A180405, then a(n) is prime. It seems that the converse is also true: if a(n) here is prime, then n is in A180405.

Indices of composite terms are given by A363379.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Neal Gersh Tolunsky, Graph of first 36568 terms

Cf. A180405, A363379.

cp's OEIS Frontend

A180405 Smallest integer not yet present in the sequence such that the sum of the first a(n) terms of the sequence is a prime.

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