cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A338924 Every prime term k of the sequence is the cumulative sum of the prime digits used so far (the digits of k are included in the sum).

Original entry on oeis.org

1, 2, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 11, 21, 22, 24, 19, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Keywords

Comments

This is the lexicographically earliest sequence of distinct positive terms with this property. The prime digits are 2, 3, 5 and 7.

Examples

			a(1) = 1 as 1 (a nonprime term) is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
a(2) = 2 as 2 (a prime term) is the sum of all prime digits used so far;
a(3) = 4 (a nonprime term) as a(3) = 3 (a prime) would be a contradiction and a(3) = 4 doesn't lead to a contradiction;
...
a(14) = 11 (a prime term) as 11 is the sum of all prime digits used so far (2 + 2 + 5 + 2);
a(15) = 21 (a nonprime term) as 21 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
...
a(18) = 19 (a prime term) as 19 is the sum of all prime digits used so far (2 + 2 + 5 + 2 + 2 + 2 + 2 + 2); etc.

Links

Crossrefs

Cf. A338922, A338923 and A338925 (variants on the same idea).

Programs

  • PARI
    v=[1]; w=[]; n=1; p=2; while(n<100, for(q=vecsum(w), p,if(isprime(q), m=[]; m=select(isprime,digits(q)); c=0; if(vecsum(w)+vecsum(m)==q&&!vecsearch(vecsort(v), q), v=concat(v, q); w=concat(w, m); c++; break))); if(c==0, while(isprime(p), p++); w=concat(w, select(isprime,digits(p))); v=concat(v, p); p++); n++); v \\ Derek Orr, Nov 17 2020

A338925 Every nonprime term k of the sequence is the cumulative sum of the nonprime digits used so far (the digits of k are included in the sum).

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 25, 37, 41, 30, 34, 43, 42, 47, 53, 59, 55, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 130, 131, 133, 137, 135, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Keywords

Comments

This is the lexicographically earliest sequence of distinct nonnegative terms with this property. The nonprime digits are 0, 1, 4, 6, 8 and 9.

Examples

			a(1) = 0 as 0 (a nonprime term) is the sum of all nonprime digits used so far;
a(2) = 1 as 1 (a nonprime term) is the sum of all nonprime digits used so far (0 + 1);
a(3) = 2 as 2 (a prime term) is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
...
a(14) = 25 (a nonprime term) as 25 is the sum of all nonprime digits used so far (0 + 1 + 1 + 1 + 1 + 1 + 1 + 9 + 9 + 1);
a(15) = 37 (a prime term) as 37 is the smallest term not yet present in the sequence that doesn't lead to a contradiction; etc.

Links

Crossrefs

Cf. A338922, A338923 and A338924 (variants on the same idea).

Programs

  • PARI
    v=[0];w=[0];n=1;p=1;while(n<75,for(q=vecsum(w),nextprime(p+1),if(!isprime(q),m=[];for(k=1,#digits(q),if(!isprime(digits(q)[k]),m=concat(m,digits(q)[k])));c=0;if(vecsum(w)+vecsum(m)==q&&!vecsearch(vecsort(v),q),v=concat(v,q);w=concat(w,m);c++;break)));if(c==0,p=nextprime(p+1);for(j=1,#digits(p),if(!isprime(digits(p)[j]),w=concat(w,digits(p)[j])));v=concat(v,p));n++);v \\ Derek Orr, Nov 16 2020

A338922 Every odd term k of the sequence is the cumulative sum of the odd digits used so far (the digits of k are included in the sum).

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 11, 32, 34, 36, 21, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 71, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Keywords

Comments

This is the lexicographically earliest sequence of distinct positive terms with this property.

Examples

			a(1) = 1 as the sum of all odd digits used so far is 1:
a(2) = 2 as 2 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
a(3) = 4 as a(3) = 3 would be a contradiction and a(3) = 4 doesn't lead to a contradiction;
...
a(17) = 11 as the sum of all odd digits used so far is 11 (1 + 1 + 1 + 1 + 1 + 1 + 3 + 1 + 1); etc.

Links

Crossrefs

Cf. A338923, A338924 and A338925 (variants on the same idea).

Programs

  • PARI
    my(v=[], S=0,p=2, n=1);while(n<100, c=0;for(q=S, p, if(q%2, m=0;for(i=1,#digits(q),if(digits(q)[i]%2,m+=digits(q)[i]));if(S+m==q&&!vecsearch(vecsort(v), q),v=concat(v, q);  S+=m; c++; break))); if(c==0, for(j=1,#digits(p),if(digits(p)[j]%2,S+=digits(p)[j])); v=concat(v, p); p+=2); n++); v \\ Derek Orr, Nov 22 2020
Showing 1-3 of 3 results.

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