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 1-4 of 4 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

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

A338923 Every even term k of the sequence is the cumulative sum of the even digits used so far (the digits of k are included in the sum).

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 10, 12, 29, 31, 33, 35, 37, 39, 41, 20, 43, 45, 47, 49, 40, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 75, 77, 79, 80, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 130
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.

Examples

			a(1) = 0 as 0 is the sum of all even digits used so far:
a(2) = 1 as 1 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
a(3) = 2 as 2 is the sum of all even digits used so far (0 + 2);
a(4) = 3 as 3 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
...
a(17) = 10 as 10 is the sum of all even digits used so far (0 + 2 + 2 + 2 + 2 + 2 + 0);
a(18) = 12 as 12 is the sum of all even digits used so far (0 + 2 + 2 + 2 + 2 + 2 + 0 + 2);
a(19) = 29 as 29 is the smallest term not yet present in the sequence that doesn't lead to a contradiction; etc.

Links

Crossrefs

Cf. A338922, A338924 and A338925 (variants on the same idea).

Programs

  • PARI
    my(v=[], S=0,p=1, 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

A338938 a(1)=0. For n >= 2, let S be the sum of all nonprime digits in a(1), a(2), ... a(n-1) and let P be the next prime not already in the sequence. If S is a nonprime number less than P and not already in the sequence, a(n) = S. Otherwise, a(n) = P.

Original entry on oeis.org

0, 2, 3, 5, 7, 11, 13, 17, 4, 8, 16, 19, 23, 29, 31, 37, 41, 43, 47, 53, 56, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257
Offset: 1

Views

Author

Eric Angelini and Derek Orr, Nov 16 2020

Keywords

Comments

Similar to A338925, however this sequence does not include the nonprime digits of a(n) itself.
Each nonprime term is the sum of all nonprime digits of each previous term.

Examples

			a(9) = 4 since the sum of the nonprime digits of the previous terms is 1+1+1+1 =  4 and 4 is less than the next prime, 19.
a(10) = 8 since the sum of nonprime digits of the previous terms is 1+1+1+1+4 = 8 and 8 is less than the next prime, 19.
a(11) = 16 since the sum of the nonprime digits of the previous terms is 1+1+1+1+4+8 = 16 and 16 is less than the next prime, 19.
Now, the sum of the nonprime digits of the previous terms is 1+1+1+1+4+8+1+6 = 23 (a prime number). So a(12) is the next prime number in that hasn't appeared, meaning a(12) = 19.

Crossrefs

Cf. A338925.

Programs

  • PARI
    my(v=[0], w=[0], n=1, p=1, m, c); while(n<125, q=vecsum(w);m=[];p=nextprime(p);c=0; for(k=1,#digits(q),if(!isprime(digits(q)[k]),m=concat(m,digits(q)[k])));if(!isprime(q)&&(q
Showing 1-4 of 4 results.

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